Hi, I work in CAMHS.
I’d just start by talking to her and trying to understand what lead to it, what the self harm was “for” (eg distraction, self-soothing, suicidal etc). Ask her how she felt after it, if she still has thoughts of doing it etc. And what she did, what she used etc.
Self harm is often a coping mechanism, so it’s worth getting an understanding of the trigger(s), how she copes, what other ways she has of coping. And then exploring alternatives to self harm (talking, distraction, rubber bands etc etc).
Provide a calm, safe environment to talk through these things. Try not to get upset in front of her, and be understanding and comforting.
Remember that self harm is not the same as suicide.
It’s fine to go to GP, although CAMHS may not necessarily be required (or either the right service). Self harm is not necessarily a sign of mental illness per se. That’s why it’s important to understand triggers and address them, rather than rushing to medicalising it.