I’m assuming she’s a 16 year old in college/6th form as opposed to high school? As you mention exams, assuming GCSE. I used to work on a support help desk at my university & do initial chars/assessments for students. Obviously a bit older but the same principles apply.
I think this is a really normal age for teenagers to start really gaining independence & trying taking control of their own health & lives to a certain degree. I can distinctly remember arranging my own appointments to discuss going on the pill at 16/17 (due to horrible periods & acne) & not involving my parents. I considered myself far too grown up to need my parents permission. In reality, I was just quite embarrassed to talk about heavy periods & acne with my mum at that age!
Yes, technically she’s under your care to 18 but she’s a young girl growing up & making some of her own choices about her body, mind & well-being. It’s great she has felt comfortable enough to speak to her school & GP. Many teenagers just internalise mental health issues. So look at the positives there. The GP hasn’t done anything wrong. 16 is the age of consent for medical treatment in the UK & because of this, your daughter had the right to discuss & choose treatment confidentially. For a 16-18 year old, the GP should weigh up if involving parents is in the minors best interests (considering things like violence, abuse, sexual abuse or trauma etc) but chances are, they’ll keep the visits & info confidential to your daughter.
The school I know less about obviously. But again, I imagine they work on similar principles of confidentiality to encourage their students to feel like they have someone to talk too who isn’t a family member.
As a parent, it’s a fine line between letting go & still asserting some control. I don’t think being cross or upset at your daughter or her school/GP is the best option here. You’ll push her away. Instead, I’d be trying to find a way to communicate and discuss the medication she’s on & the possible alternatives etc. But it’s her choice as to what route she takes. I really don’t like the idea of meds at 16 either but try to find out why she was offered them, why she chose them, did anyone talk to her about counselling? See how open she is to stopping the meds if the side effects are awful, talking to her GP about different ones or referrals etc.. do this however you can. Face to face, text, WhatsApp, email.. just try open those lines of communication somehow!
Good luck, try to remember how you felt as a teen & how you reacted to your own parents at that age. Your daughter has at least reached out to someone & acknowledged she needs some support. Hopefully, this can all turn round to a positive & the main aim is for her to feel better!