My DD self harmed, fairly severely for just over two years, between 14 and 16 years old. CAMHS weren't interested (sorry, OP, I know that's a negative things to say) and after we finally got an assessment (after DD was hospitalised overnight for increasing suicidal ideation) they basically said she wasn't ill enough for her to access their support (and before anyone jumps on me I KNOW they have funding issues but as a parent I was completely distraught).
It was properly hideous, she was honest about her cutting and I was therefore able to help her manage her cuts and keep them clean and the whole process hygienic but honestly, buying fresh razors so she at least cut with clean, sharp blades was REALLY difficult. Ironically, the openness about her feelings and her cutting and our ability to 'manage' this was one of the reasons CAMHS gave us for not being able to support us. We had a good risk management plan, apparently...
Long story short, we were fortunate enough top be in a place where, with some help from my parents, we paid for her to see a private adolescent psychiatrist who diagnosed her, medicated her and gave us a recommendation for a therapist. Best money we ever spent. She is now 21, finishing Uni and about to start a Masters. There was a significant period of time where I didn't;t think she'd still be alive o her 18th birthday.
On the confidentiality thing, I had no right to the content of her sessions and the therapist was very clear that she would only be in touch is she believed she was actively suicidal (which she was, for a while) but the content of her sessions I knew, and know very little about. As PPs have said, the point of therapy is that it is confidential.
I spoke to someone at Papyrus, who are a suicide prevention charity but I mainly spoke to them about self harm. Young Minds also offer support and strategies for parents. However I would also recommend contacting the counsellor via school to see if she can speak generally (i.e. not in detail) about how you could best support your daughter.
It's a horrible thing, knowing your child is self harming and not being able to 'fix' it. I felt like I was failing her and that something I had done had 'caused' this coping mechanism. She has told me that neither of these beliefs were true. Even now, however, she can't answer the 'why' question, it's such a big thing to try and articulate a response to.
I wish both you and your daughter the best, OP. I felt angry/sad/hurt/scared and a mass of other emotions. Please try to find some support for you as well, that way you will be able to support your DD as you both work through this time. All the very best.