Well I have opposite reaction to birth control. It actually helps me get my period. I have P.C.O.S.
And yes, If you were sexually active before going on birth control. Your likely to get pregnant. If from what I understand the window of opportunity was small then the likely hood of getting pregnant would be smaller. Does that help any?
Yes, it's possible that you could be pregnant. It's always a possibility. Likely? No. You didn't miss any pills, so that means your risk is low.
Here's my understanding of fertility, etc. Day 1 (of the typical 28 day cycle) is the day you start your period. Most women ovulate mid cycle, or around day 14. Ovulation means an egg is available to be fertilized if sperm are there to seal the deal. If no sperm show up, the egg is unfertilized, and the uterus that has been building up an environment for implantation isn't needed so you get your period. Now, sperm can live up to 5 days post-ejaculation in the right conditions (inside you). So, if you had unprotected sex even a few days before ovulating, it's possible that you could be pregnant. But you said that you had been taking your pills, so it's unlikely to have happened in your case, since BCPs are designed to prevent ovulation.
For the sake of argument, let's say you were supposed to begin your period on June 1st. If the pill didn't work, we would expect that you would have ovulated May 15th or so and again on June 15th. If you had sex on/around these dates, you have a slightly increased chance of being pregnant. To be sure, take a pregnancy test. If you don't have any other signs/symptoms of pregnancy, you are probably not. If you are still concerned, go to your doctor, who will give you the HCG blood test which will tell you if you are pregnant, with more accuracy (and sooner!) than a urine pregnancy test.
Hope this helps!