Hello,
First of all, I am so sorry to hear about your daughter's pain. Reading your post made me tear up a bit because my story is almost exactly the same as your daughter, and I know how hard my mom has worked over the years to help me. I got my first migraine just after turning 17 years old and missed school from mid December all the way to mid March. I am 23 years old now and still struggling to figure out my situation. I don't say that to scare you but to let you know that I understand your desperation to figure out your daughter's health.
I, too, had braces when I first started getting migraines but had had them for over a year before that. We chose to take them off early because every time they were tightened I was left with a 9-10 migraine for days. I do suggest approaching the headaches in a multidimensional way. Maybe speak with her orthodontist and a neurologist and see what they both say about the pros and cons of removing the braces in order to try more tests.
Another thing I wanted to bring up to you is mental health. Before I got migraines and even the first month or so into my migraines, I would've been the last person to see a psychiatrist or therapist. However, once I started seeing a psychiatrist (unhappily at first) I realized that all those days in my bed for months had caused depression and anxiety. Once we got those under control I was able to better manage my pain. Enough to get back to school 2 or 3 days per week, which is a huge improvement on missing every single day. My experience with migraines actually led me to pursue and earn my BA in Psychology.
Even though I haven't figured out my migraines yet, I do hope this information helps you and your daughter. Looking back, I realize the loneliness of migraines was the hardest part to deal with I high school. I wish I had somebody around who could relate. I think talking about the problem is highly important, whether it be with a professional or in a migraine support group (with your consent and supervision of course).
Good luck! You both are in my thoughts!!