Taking pill in middle of irregular period ?

During the first week of my period back in late December I had really heavy flow with large blood clots. It was so bad that I was in complete discomfort since I could feel every time a blood clot would come out. I also had trouble with leaks over night, even with an overnight pad. The period lasted for a week and some four days. I was good for two days, then the following day I began to bleed again but it was light enough to only use a panty liner. Three days later I had to switch to overnights again. It's been two weeks now but my period wasn't as heavy like the last time but blood clots continue to come out (although smaller). My gynecologist prescribed me Aviane birth control pills but I don't know if it's ok to start while I still have my period. I have no idea when it's going to finish, there doesn't appear to be any signs of stopping. Also, after taking the reminder pills does that mean my period will come back and then when it finishes, I start a new pack? This is my first time taking birth control, please help!!