Might i possibly get on birth control without my parents knowing?

Depends on age : This depends on your age and the state you live. Planned parenthood is a good place to start. It is usually best to discuss these things with your parents. They may not like it but they will want to prevent being grandparents.

Yes: You have the right to privacy. You can go to a doctors office or planned parenthood and expect them to keep your visits confidential. If you bill the visits to your parents insurance they would probably ask you about the bill...