Implantation and period question?

So I’ve had this weird fear. I started my period on birth control this Tuesday and I have this fear that a fertilized egg implanted Sunday or Monday and it’s surviving my period. Is that even possible? Or is that too late for implantation to happen and still survive.

If an egg has implanted in the uterus and a period occurs, will the egg get shed out too? Or is it possible that it sticks?