AFAIK, if you're not at risk of suicide/doing high-risk self harm (e.g. moderate drug misuse, severe burns) and are over 16, they should be bound by confidentiality.
Maybe that's only if you and them have discussed it formally though - I mean, how would they know you are not suicidal/doing extremely high risk self harm without talking to you?
Telling school and your parents about your self harm is the best way forward. Recovery is infinitely easier and longer-lasting if you have a good support network in your family and school life.