Is is possible to be pregnant and have a period

Patient: Last time I has unprotected sex was in mid August I’ve had periods that last 2 days sometimes 4 but today I had a discharge with a very very small bit of blood in it kind of how it looks when your mucus plug starts to break loose I’m wondering could I be pregnant and still having a period or what?

Symptoms: Tired, heavier eating, spotting in discharge, back pain, headaches, cramps shortness of breath