Will my parents be informed about self-harm if I'm in sixth form?

I've been 18 since last year and I'm doing my A-levels in a bit. Since the reasons I self-harm are sometimes related to academics and grades, I seriously think I need to tell someone before my exams start, because I don't want self-harm and all of my other worries to bring me down. A-levels are stressful and, especially if an exam goes badly, I don't doubt things will get too much at some point. I'm already an adult but I have a feeling the school's safeguarding policy still applies, so I'm worried they'll tell my parents (who will absolutely not react in any helpful way). I've never hurt myself badly enough for my life to be in any risk at all, and I don't feel like hurting anyone else. Is there a pretty good chance they'll tell on me?