Can a woman get her full period(7 days of bleeding, but with clots) and be pregnant without knowing?

No...: Having a normal, regular period means one is not pregnant. Having sex after the period means one could become pregnant on the current month. If the next period comes and is a normal regular one, it means one is not pregnant, again. If worried or if one's period was not "normal or typical," one can do a urine pregnancy test the week after starting the abnormal period, or 3 weeks after having sex.