There are different kinds of birth control so tell your doctor and they can try a different prescription.
True. It does take at least 7 days for most birth control pills to become effective.
When did you start taking the pill? If it was when your period started then you'd be unlikely to become pregnant 3 days after. You don't normally ovulate until between about days 11 to 16 of your cycle. Sperm can survive up to about 5 days.
You likely are having a "withdrawal bleed" from the pills.
Hope it helps.