Had unprotected sex on Saturday 27th August. I got my period the next morning but only for 3 days. Am I pregnant? And is it too late to start birth control pills?

As you only had intercourse a short 4 days ago, it would be impossible to tell if you are pregnant at this point in time.

Yes, it would be too late to start taking birth control pills. You are now going to have to wait until next month to see if your period comes.