I've been having mild cramps here and there for about 4 days.. that kind of feel like my period (5 days after I had unprotected sex). I'm not supposed to get my period for another week. I've also just felt really exhausted and I've noticed my gums are really sensitive and have been bleeding when I brush my teeth, which hasn't happened to me before. Is it possible that I could be pregnant?

Bleeding gums isn't a sign of pregnancy. Nor is exhaustion or mild cramping.

Wait until you've missed your period, the best symptom of pregnancy. If you miss it by two weeks then take a home pregnancy test. Until then no one can really say if you are or not.