How works the menstrual cycle? Can you get pregnant after fertile days?

Yes. There is a span of a few days where you can become pregnant. The egg survives around 24 hours after ovulation, and sperm can survive longer for up to a few days in the female. Therefore, unprotected sex a couple days before or after ovulation can lead to pregnancy under the right circumstances.
Periods. Normal menses is 9-10 times per year (every 3- weeks), last 1-8 days. You have period when estrogen and Progesterone drops at end of cycle (withdraw bleeding). Ovulation occur when you have a surge on 2 other hormones in midcycle. Physically you cannot tell with certainty when you have ovulation (fertile days). Short of abstinece you can always get pregnant. Your md could explain a bit more.