How do I convince my mom to let me start birth control?

Well, explain your "girl reasons" to her. I know she may not want to talk about it, she may shy away from it, she may get upset by it, but make her sit down and listen to you. I'm assuming your "girl reasons" are something along the lines of bad cramping, breakouts, extremely heavy flow... etc. There is nothing wrong with wanting to have more control over your body.