Really sorry you are going through this.
I have a teen (now 16) who has also attempted suicide and whose mood swings are very strong and have a great impact on the family. I can relate to what you say about getting angry: it is so difficult when a low despairing mood that has kept the whole family under a cloud for days is suddenly replaced by a high. But dd is getting better at verbalising how she feels and is beginning to realise that the high moods are as much part of her anxiety as the low ones, and I am getting better at spotting when what seems like irritating insouciance is in fact a sign of anxiety-triggered hyperness.
I have learnt never to confront her about pain. One of dd's big problems is that her physical chronic pain condition was mistaken for psychosomatic pain when she was younger, so she has learnt not to trust anyone on the subject of pain.
Instead the approach CAHMS and I take now is that it is rotten to have this pain, but that it is possible to make it more bearable by using certain techniques. When dd and I have discussed it I have compared it to the pain of childbirth: nobody denies that it hurts having a baby, but there are mental techniques you can use to make it more bearable. I have learnt never to try to analyse her pain.
(And to be frank, when I get a tension related headache or migraine, I wouldn't find it particularly helpful if dh told me it was all in the mind. Of course it's in the mind, in the sense that it's my worries that cause the pain. But the migraine is still there and it still hurts and having it analysed doesn't make it hurt less.)
Is your dd still seeing CAHMS?
What my dd found useful was that their approach was very much about putting her in charge, giving her the tools for taking charge of the situation. It is taking a long, long time, but I can see the light at the end of the tunnel. Dd started anti-depressants last year when she turned 15 and they have taken the edge off it, not to the point of making her happy, but to the point where she feels able to confront life to some extent. It is also helping that she is becoming mature enough to discuss the situation openly, and I try to make sure that there is no stigma or embarrassment about it. CAHMS have told her that she may always have these mood swings, that this may be part of who she is, but that she can learn to live with them so that they do not get to dominate her.