How can I manage my 17 year old daughter's behaviour?

It is clear that you love your teenage daughter and are very worried about her. As a parent, the most loving thing you can do for your child is to say NO. The worst thing a parent can do is to avoid saying no for fear of upsetting their child. No can be said in firm and loving ways. Children and teenagers need healthy boundaries, and although they may kick and scream, on some level they know that it means that you love them, and they feel safe.
This is more complex with teens as they are exploring and expressing their individuality and to a degree this is healthy for them. However self harm suggests low self-esteem and a cry for help. As much as teens want to become independent they still need to know that parents love them and are there for them. Social anxiety also indicates low self esteem; and the teen years are a particularly vulnerable time. It sounds like your daughter needs lots of love and confidence building.
I highly recommend that you find professional counselling support in your area. Some reading materials that can help: A great online resource is http://abcdparenting.org/. For more indepth reading, Systematic Training for Effective Parenting (STEP) for Teens (http://www.steppublishers.com/) by Dinkmeyer is a very useful guide for parentswith homework exercises to help you apply the principles. These are very challenging years; I wish you all the very best.

In addition to the advice already received, including finding a professional counselling support in your area, you may also start with at least two steps:

1. Eliminate or minimize your role in intense interactions: Assess how you manage the intensity of interactions with your daughter and in general. Start watching and managing your reactions in tone, voice, internal emotions in order to achieve  emotional detachment both on the outside and on the inside, a calm , though lively tone, using a low-pitched voice can show dramatic effects in interactions and hopefully in those around you. This is different from choosing passive-aggressiveness.
   
2. Spend as much time around the house as possible: This might be difficult as teenagers might not interact at all, and you might wonder why do you even plan on stying at home, or teenagers might continuously seek intense interactions, leaving you with no sense of peace and privacy. That’s why point one is very important. Just be around the house, ready to listen more then reacting with an answer to any comment or provocation. Make sure that you do something useful while staying at home and not just go to your room to sleep or staying on the couch to watch TV by yourself. Join them in watching and choose to do something – cutting vegetables, sewing, ironing, knitting, correcting work papers while still being there.
   

I agree with Dr Natalie Parletta sometimes saying no is the best thing to do with children and teenagers, they do need strong boundries and as much as some may rebel saying no shows them you care. Tough love is sometimes the best with teens.

I would also suggest you talk to her about counselling as self harm is something that needs addressing, it can show that there are other underlying issues your daughter is struggling with. It would be helpful to find someone she can talk to.

There are a few different issues you raise that may either be related or present for different reasons. These are social anxiety, self harming, tattoos and piercings. Empathy is the key. Taking time to understand the stresses and concerns of your child no matter how old they may be is a tough path to try and work through as a parent. The self harming and social anxiety suggests your child is under a lot of emotional distress. There is clearly a lot getting her down. Setting the scene to try and hear what life is like through her eyes can be quite a challenge and possibly difficult to hear… but can be quite powerful if your daughter feels she can share her heart without being judged. The self harming suggests that her mindset and emotion may be in a dark and heavy place. Something that really needs professional help. So connecting in with a psychologist is vital. Feel free to email if you would like to talk this through more.  

Having worked with a number of teens I often behavioural issues stem from self-esteem issues and one of the best things you can do for her is to help her access her skills and creativity and express them in functional ways. 
We all do behave in certain ways in order to be noticed and acknowledged and if you can find a way for her to communicate her needs to you without fear of judgement and build her esteem then you should find that the communication between you is improved and so is her desire to express herself in a functional way. 
From a Kinesiology/Chinese Medicine perspective we could view this as a disorder of Shen and the best way to help with Shen dysfunction is through connection with others. I would suggest you seek some form of therapy for her in which she can build a trust based relationship with others, ths could include counselling, kinesiology or psychology. She may also benefit from belonging to a group who share similar interests to her, i.e art based, sport based etc.  

Others have already offered sound advice but I would just like to address the issue of  you being scared to say no.  I would suggest that, while it's difficult to say no and possibly upsetting for your daughter, if you believe that is the right response for you and for her well being, then you need to do so.  By standing your ground on issues that are important, you are giving your daughter the message that you care enough to withstand her anger/distress and she will appreciate this down the track even if she does't seem to now.  Regarding issues of tattoos and body piercings, sometimes it can help to put a time frame on it  ie. you can make that decision for yourself once you are 18. 

Wow, thanks for that Grant, wish I had known about this book when my girl was a teenager! It looks like a must-read for parents of girls - for the mum here is a blurb from the UK Book Depository (available online for $16.34 with free shipping):

Steve Biddulph's Raising Boys was a global phenomenon. The first book in a generation to look at boys' specific needs, parents loved its clarity and warm insights into their sons' inner world. But today, things have changed. It's girls that are in trouble. There has been a sudden and universal deterioration in girls' mental health, starting in primary school and devastating the teen years. Steve Biddulph's Raising Girls is both a guidebook and a call-to-arms for parents. The five key stages of girlhood are laid out so that you know exactly what matters at which age, and how to build strength and connectedness into your daughter from infancy onwards. Raising Girls is both fierce and tender in its mission to help girls more at every age. It's a book for parents who love their daughters deeply, whether they are newborns, teenagers, young women - or anywhere in between. Feeling secure, becoming an explorer, getting along with others, finding her soul, and becoming a woman - at last, there is a clear map of girls' minds that accepts no limitations, narrow roles or selling-out of your daughter's potential or uniqueness. All the hazards are signposted - bullying, eating disorders, body image and depression, social media harms and helps - as are concrete and simple measures for both mums and dads to help prevent their daughters from becoming victims. Parenthood is restored to an exciting journey, not one worry after another, as it's so often portrayed. Steve talks to the world's leading voices on girls' needs and makes their ideas clear and simple, adding his own humour and experience through stories that you will never forget. Even the illustrations, by Kimio Kubo, provide unique and moving glimpses into the inner lives of girls. Along with his fellow psychologists worldwide, Steve is angry at the exploitation and harm being done to girls today. With Raising Girls he strives to spark a movement to end the trashing of girlhood; equipping parents to deal with the modern world, and getting the media off the backs of our daughters. Raising Girls is powerful, practical and positive. Your heart, head and hands will be strengthened by its message.

As far as your daughter's self-harm is concerned, she may find this support forum helpful: http://buslist.org/phpBB/index.php

I don't self-harm but am one of its volunteer administrators.

This is all fantastic advice. The ‘Raising Girls’ book is particularly amazing. I would also reccomend reading The Anatomy of Peace by the Arbinger Instutue. The book details a few families attending a family workshop while their sons or daughters are on an outdoor adventure therapy program. Its a really exciting look into how parents can build new relationships with their children when there as been stress. 

I also agree with what Kristen Ross mentioned about self-esteem. When we can get our teenagers to feel good we'll often get a better output. You've mentioned that she is working with a doctor, have you seen any positive outcomes of this? 

Relationship is essential before behaviour.

Try this watching this video:

http://www.youtube.com/watch?v=eVDMATVzhTk

Best wishes