All right , so I was on vacation &; I started my period on the 16th?
& I had sex probably about 13 days later from the day I started is it possible that I could be pregnant?
I usually have my period every month during around that time

If you had sex, then it's possible that you're pregnant. Even birth control isn't 100% effective. If you think you might be pregnant, then take a test or see a doctor.

If you had sex ( even protected) there is always a chance, if it was unprotected sex it is even a greater chance. Only properly taken HPT ( or doctors visit) can tell you for sure