I think that what happened is that when you missed the pill it caused your period to begin early. It takes 2 weeks after intercorse for incest to occur so it just add up. The egg probably got to the uterus but since you were taking bc, it could not attatch itself to the uterus wall and was expelled immediately.
It is possible that you miscarried. I lost 5 and only had one D&C for the one that was almost at 5 months. If you can, see a gynecologist. He/she can determine if you will need a D&C. And can tell you how to take care of yourself should you become pregnant.
Urgent care is not the place to go, as you found out. There is really nothing they can do so they will send you away - go to a gyn as soon as you can.
Wishing you the best