If it's any consolation, breaking down in the appointment isn't necessarily a bad thing. I hid a lot of things early on, it made getting help quite difficult - my family wouldn't believe me because I seemed stable, professionals could only work with what I was giving them. Save yourself some time and suffering and be honest.
I've done the breaking-down-in-appointments too, at worst the doctor isn't equipped and refers you on, or the experience of crying is a bit uncomfortable. Ideally you've gotten something off your chest and the GP is understanding, and can direct you towards professional help or at least provide some counsel. If you feel like falling apart is a probability, clearly some emotion needs out (let it out in a safe environment with a trusted third party who doesn't require your mask of stability).
Try not to fear "breaking down" with the GP, this is the best place to do it. I imagine for a long time you've held it together for your daughter, for any other family, friends, and work. You're going to the doctor for YOU, there's no reason to act strong to your own detriment there. Do your best to be fully honest, even if it feels "dramatic" - it still means somethings, indicates your state of mind, and will lead you to the most useful resources which you would otherwise miss by downplaying your issues.
As a side note, I struggled in my teens with MH problems too, my mother getting MH help would have helped a ton. Your daughter likely wants to see you well too, don't get stuck in a cycle of holding back from eachother trying to reduce the burden on one another, and then letting it all come to an emotional head when your cups overflow. You're doing a good thing by helping yourself too.
Best of luck x
