Can doctors prescribe the pill just for your period?

Of course: B c pills have many non contraceptive benefits including shorter and lighter period, less cramps, decreased chance of getting a cyst, i recommend a workup to see why the periods are heavy and there are other meds to lighten the flow like Lysteda and at your age you may want to consider after you have had a proper work-up, endometrial ablation, I do them in office works well.