Help! Could I possibly be pregnant?

Okay, here's the deal, I recently started taking birth control about a month ago and few days before that I had unprotected . I noticed that I was feeling sick to my stomach and I'm constantly tired and I was even having cramps way before it was time for my period. I'm still feeling tired and have a weird feeling on the lower left side of my abdomen. I started my period yesterday, but someone told me when you're on the pill, you don't have a real period, that it's a hormone with-drawl bleed. Is this correct? If so, could I be pregnant?