Hello,
Welcome to ehealthforum and thanks for writing
Birth control pills take 1 to 2 weeks to provide contraceptive effect and if immediately after starting them unprotected intercourse is performed then pregnancy is a possibility.Did you start the pills after the periods as you have mentioned that you also had contact during ovulation before starting them.
Another reason for spotting could be because of pill use as irregular periods and spotting is a common side effect while on them.Kindly visit a Gynaecologist for evaluation as conception chances are present.Get a Urine test done for pregnancy determination.
Take care!