Mirena IUD question...?

Mirena is not just used to prevent pregnancy but also to slow down a very heavy menstrual cycle(which I have). My gynecologist will not do a hysterectomy because he says ,"God put those organs in there and he will not take them out unless they are a threat to my life." He will not do an ablation. I have already had a D&C and it didn't work. I am taking a medicine(and forever will take it) that I am not supposed to take birth control pills with. (levothyroxine is the medicine). Does mirena contain the same thing that birth control pills have? I have got to do something to control these extremely heavy periods. I already have to take prescription iron pills. I had to go to the hospital before and they had to give me blood because of this problem. I just don't know what else to do. Anybody got any answers? Could I get the mirena? I am not worried about pregnancies because my tubes are already tied.