If someone says they're having mental health problems it should be taken seriously b their loved ones, even in teenagers. A professional could assess her and say what help she needs, if any.
I was pushed aademically but with no emotional support, I didn't feel I could discuss any problems I was having with my parents. I was under CAMHS briefly at 15 until I stopped going because the consultant who was supposed to be supporting me stopped being supportive.
I got a 1st from Birmingham eventually, though I had to drop in and out a few times with largely untreated mental health problems. I've never really been able to work due to severe mental health disability.
What would've helped was warmth at home and school. If my parents had tried to get my MH problems treated as early as possible (they could even have pushed for it at 16/17. when I dropped out of college before going in again, and sent a year not doing anything because I didn't have the confidence to work.
I kept telling them/hinting at having depression or anxiety/stress, but they would ignore, laugh at it or be in denial, or make me feel bad.
The earlier it's treated the less likely it is to effect someone in later life. This is a chance to nip it in the bud- please take it.
I've had a great relationship with my mum since she split up with my dad when I was about 17 btw. She was able to show the warm, caring person she is, which she didn't when she was with him.
Either way- best wishes and try not to blame yourself. Lots of people are prone to MH problems, whatever their parents do. All you can do is do the best you can for her now, and be proud of yourself for that. xxx