hii, what your daughter does seems very familiar to what I did.
I've a depression and anorexia/boulimia. I think you should let her talk to a psychologist. Or maybe just someone like me, who's dealing with it too. Just to let her know she is not on her own, and there are "nice" treatments for this problems.
keep in touch with me if you like :)
xxx
It certainly sounds to me like you should be concerned.
From what you describe, I would be suspicious about bullying. The combination of this new isolation, self-harm behaviour and a sudden nose-dive in self-esteem and body-image is suggestive; obviously there's school, but you've probably asked her teachers already. Are there any after-school groups, clubs or anything your daughter attends? It might be worth asking questions there too, but unfortunately these days bullying can take place without any adult being aware of it.
If possible, try to have a look at your daughter's facebook account; her privacy settings might make that difficult if you don't have her password, but see what you can find out. If you can, have a look at her mobile too; her text messages might be informative.
With respect to getting your daughter medical help, that's more problematic if her behaviour is already self-destructive. I think the key here is probably patience and empathy rather than force; if your daughter is suffering from anorexia then she already has issues with control, so if she feels that you or anyone else are trying to force her into anything - anything at all, however trivial - she's likely to throw up walls, as happened when you took her to the doctor. If it keeps happening, in fact, it might well make her anorexia worse as that is an illness all about controlling one aspect of life because everything else feels out of control.
The thing to remember is that she is still a child and that there is a big part of her - whether she knows it or not - that desperately wants to tell you what's going on so she won't feel so alone with her problems, whatever they may be. If I were you, I'd wait until you and she have some peace and quiet, and gently but firmly state - don't ask, state - that she's not happy and that it's making you unhappy because you love her. You need to be calm about this, because if she feels manipulated emotionally you won't get anywhere. Control the conversation, and make it clear that your only concern is her happiness; she needs to understand that you're not angry about her grades or her behaviour, and that they only bother you because they show she's unhappy. I can't emphasise that enough; she needs to know that YOU don't care about bad grades or swearing or slammed doors or whatever else she's been doing, because none of that is as important as she is. I guarantee there's some guilt in there somewhere about the way she's been acting, and if you can lift that guilt - or even just some of it - the relief might be enough to make her open up a little.
If she gets angry or leaves the room, let her. Again, if she feels like the conversation's being forced on her she'll just clam up. Let her be angry, leave her in peace to calm down, and wait until next time you and she are alone and the mood's peaceful before you start up the conversation again; you may find that once she's realised you're not going to force her to talk she brings it up again on her own.
If she responds well to what you've said though, ask her - don't order her - if she'd like to talk to you or to a doctor about whatever's going on; if she feels she's "gotten out" of talking to you about it right now, you may find her quite agreeable to the idea of talking to someone else later on. Again though, if she wants to suspend the conversation at any point you need to let her.
If she talks to you, all well and good but be sure to remain calm and non-judgmental no matter what you may hear from her - but you need to make sure she doesn't think you're belittling her problems either; remember that what seems utterly trivial to an adult can be very scary to a child.
If she agrees to see a doctor, offer to come with her or to drop her off and wait in the car, let her choose when she wants to go as far as possible, even let her choose which doctor to see if that's appropriate - try to hand her as much control over it as possible within the boundaries of making it gently clear that once she's promised to go you expect her to do it. Again, reassure her that no one is going to make her do anything she doesn't want to; they're not going to force pills down her neck or make her tell her deepest, darkest secrets.
Basically:
1: Make sure she knows you love her no matter what.
2: Try not to let your anger/disappointment show about things like her grades - increasing her guilt or the pressure she feels under will only make her withdraw further.
3: Don't force anything (the obvious exception being if she's about to harm either herself or someone else).
4: Let her have control over as much as you responsibly/safely can.
5: Have patience. Whatever this is, it is unlikely to be resolved quickly; but you can get there, and your daughter can recover.
Best of luck with it anyway; sorry this answer's so long, I was trying to be really clear.