How can I convince my mom to let me take birth control?

I’m not currently sexually active, but i have horribly irregular periods (sometimes as often as 2-3 times a month, or only every other month) that worsen my depression and anxiety to the point that I’m often suicidal (I already take antidepressants, and they are helpful otherwise) and I get awful cramps/migraines/exhaustion (I usually have to miss a few days of school every month because I can’t stay awake and I’m in too much pain). My doctor has already recommended birth control for me, and I’ve been begging my mom for months to allow me to take it, but she is extremely against it. I know I could get a prescription without her knowing, but I’m too afraid because she occasionally searches my room, bags, etc. and if I were to go against her on such a “big” thing (in her eyes), I’d probably be grounded until I’m 18 in 11 months. What are some things I can try to do to convince her otherwise?