Honestly, your decision to go on the pill (provided you're paying for this yourself) is between you and your doctor.
Think about it like this; How would they react if they found out you were pregnant? Instead, in wanting to go on the pill and using condoms, you're thinking ahead and being responsible, and that's to be commended.
So, if you can get yourself to the doctor and pay for the pills yourself, i don't see what your parents have to do w/ this. If you're relying on your parents for birth control, you can try talking to them, but you may be out of luck.