[hocus pocus]

It probably differs depending on where you are, but with my experience, therapists are required to tell your parents (if you are under eighteen) about your self-harm if they don't already know about it. My parents already knew about mine so my therapist keeps everything confidential. A therapist usually won't tell the parents anything else outside of that initial time but it depends on your therapist.

You could always ask your therapist what their confidentiality policies are, but if you're uncomfortable with that, you could talk about a "friend" in a similar situation and see what they have to say. I've done that in therapy a few times and I have found it helpful.