The first day of last period was Nov. 5th. I had unprotected sex three days later and again last night and today. My fertility window is approximately Nov 15th - 21st. Today is the 13th and from my understanding sperm can live inside you for several days. Could I be pregnant?

It would be too early to tell if you are pregnant at this point in time.

You are right in that sperm can live 3 or more days inside before "meeting" up with the egg.

You are now playing the waiting game. You should wait to see if your period comes. If it does not test using first morning urine.