Hey, whenever you have sex there is a slight chance that you could be pregnant. But, having your period is a good thing, it means the egg is leaving ur body. I've read that sometimes, even during pregnancy, women have their periods for up to 6 months after conception. Whether the info is accurate or not, this is the only advice I can give you.
You're right the pill most times isn't effective for atleast a month after you've begun taking it regularly.
Be sure to take a test as soon as possible, and look for early warning signs of pregnancy. (for ex., swollen/tender breasts, darkening of the nipples, missed periods, morning sickness, etc.)
best of luck, hope things work out for the best.
-k.