Question on birth control?

I'm 20 years old and yesterday me and my boyfriend had unprotected sex. He never finished in me or anything like that and he wasn't close to finishing, but I don't want to risk anything like that again. I want to get on birth control and I'm going Later this week to talk to my gyno to talk about some options. My problem is, I still live at home. If either of our parents found out we would be in huge trouble and not be allowed to see each other. Will I be able to get on it without them finding out? I'm on their insurance still, but I have a job and so I could pay for the prescriptions and the copay. 

My mom knew I was going this week but she thinks I'm wanting to go just for a check up. If I tell them I want my information confidential will I be able to get on birth control with out anyone finding out?