How to get birth control?

So I'm 17, and have horrible period symptoms. Vomiting, horrible cramps and migraines. I've been to the doctor and they have said the best thing would probably be to be put on birth control. However my mom thinks birth control will give me cancer and will not put me on it. I know there are ways to go about getting it on my own but I'm not sure how it works, and I don't work. Does anyone know the best way for me to get put on the pill?