How do I bring up the topic of birth control?

So, my period has been progressively getting worse and worse each time it comes around. I've gotten to the point of feeling like I will pass out or throw up, and there has been times where I cannot get out of bed because of migraines and cramps. Last month, it was late by a little over a week (from what I assume was the extreme stress I had because of exams and school in general), but it came and lasted its normal amount of time (5-7 days). Today it began and it is extremely heavy. So much so that I bled through the underwear and shorts I was wearing, I've always had pretty heavy periods, but this is the worst I've ever had by far. Would birth control help with the pain along with the heaviness as well?  
I guess I should include that I'm 17, turning 18 in 3 months. I'm still under my parent's roof, on their insurance, which means that I can't go to the doctor unless my mom knows and agrees that it's time. I'm worried she will think that it's only because I have a boyfriend and we want to have sex, but we don't actually do it. I'm worried she won't trust me enough to agree to take me to the doctor. But if the birth control could help, how should I bring up that I think I need to go to the doctor or possibly begin taking birth control for it? How can I convince her that it's not for the reason of having sex? 
Thanks so much!