Yes for sure you can ! I still had a period or two after I found out .
You might want to go talk to your dr for blood work but it could have been an early miscarriage or also referred to as a chemical pregnancy where you get a positive test but still have a period and lose the baby with the shedding of your period. I am not trying to be a downer but having a heavy normal period while pregnant normally isn't a good sign. Some may argue you can have a period during pregnancy but by definition of a monthly period you would shed the uterine lining along with everything in and on it. I believe you can have bleeding during pregnancy but it does not come from within your uterus. Again i would honestly go get checked by the dr just to be certain.