I need to be on birth control but my mom won't let me?

S
I am 15 and for almost a year now I have had a very heavy flow, irregular period, and extreme cramps to the point where I was throwing up from the pain. I have gone to the doctor about it and I was prescribed naproxen for cramps and other medication for nausea. I haven't thrown up since I starting taking these but my flow is still heavy and I often bleed through my underwear, even with super plus tampons. My doctor said the only option after these medications is birth control. I really want to be on it to reduce my flow but my mom clearly does not want me to. She still makes up every excuse to convince me out of the idea. It is very frustrating bc she acts like she doesn't trust me (even though she says she does). I know she is concerned about me having sex. I have no idea what to do bc I think I really need to be on birth control. However in about a month I am going to the doctor for a yearly checkup so I will be sure to mention this. Any advice??