Hey, Plumsie - just wanted to offer my support and give you ****hugs****
Welcome to RYL.
Its wonderful that you have found somebody with such an understanding of problems similar to your own. It sounds to me that your partner is perhaps not quite ready to give you the support you need; not surprising, considering they're still dealing with their own. That doesn't mean you can't talk to each other about your struggles, but you should both seek your own support networks too.
I think your parents are behaving selfishly because they are afraid - have you tried talking to your GP? Or to someone at school/college? I know they're your parents and I don't know how old you are, but you are still your own, autonomous person who deserves the help they need. Talk to someone. Your parents will understand eventually and be grateful that you were sensible enough to realise you needed help.