First, I am sorry your parents split, for when relationships end, so it's the children who feel abandoned when their parents go their separate ways. Often, feelings of helplessness and dependency come flooding in, and we are overwhelmed. This, and even fear of being alone when needing your parents' company is what has shattered your confidence, because abandonment is similar in many ways to bereavement. Except there are ways of helping yourself lose some of this awful feeling of being left, and this writing out a list of the things you miss when your parents were together. Write down all the things you loved about your dad and your mum, and also, in another columns, all those things you disliked about their individual ways.
And this is where a journal comes in so good. In it, you can write the things you said and did that you maybe regretted. Writing helps enormously these guilt things; even simple poetry.
Do you have a close friend in whom you can trust to give you support and understanding? I realise self-injuring is a private thing, so you'll most likely keep that from them. But a special friend will give you help and tenderness during your down times, and to you they would be special, because they wouldn't want anything in return.
Now you have been abandoned, it's completely normal to feel sad, depressed, etc. What is problematic, however, is when we get stuck in those places and feel wronged, often for a long time. But somehow, you have to kick back from the sadness of your parents separating to let them find their own path, while you concentrate on trying to rebuild up your trust for them, as they set out to experience being single again.
I don't know much about self-injuring, other than cutting or whatever, apparently helps release inside all that built-up tension. So the only advice I can offer here is you please keep your wounds clean, and every day until they heal, apply a dressing.
Seeing a counsellor would really help. Is it possible your doctor could refer you to someone they know is excellent? For myself I had a very good counsellor who helped me over mummy's death, so there is definitely help for you with one of these specialists.
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If you believe in yourself good things,
then go do it.