The girl I work with is 17 and has the same problems as you but she does has cysts on her ovaries. Her doctor but her on LoEstrin FE 24 which are birth control pills. The the last pills in the pack are iron pills. He also gave her prescription iron vitamins. I take the same iron pills as her they are called Hemocyte Plus.
She still has cramps right before her period but she does not bleed heavy anymore and her iron levels are much higher. Still a bit tired on her period but before she got on the BCP and the vitamins she was calling out or just about fainting at work and turn white from loss of blood.
It's worth looking into before having a transfusion. Maybe it's just me but that's kinda harsh for a first treatment for your problems.
Hope all goes well. I'll be adding you to my prayers.
EDIT: I forgot to mention that I am on the same BCP. They are the only ones that do not give me migraines but sadly I've gain 22 lbs on them. This is my 6 month and the weight seems to be slowly coming off. I am guessing that my body is finally getting use to them. I read the paper that came with my iron pills and it read that they are for the treatment of iron deficiency anemia and folate deficiency pregnancy, puberty, excessive blood loss, and advanced age. Also for treatment of conditions in which iron deficiency and vitamin C deficiency occur together, along with a deficient intake or increased need for B-Complex vitamins in chronic and acute illness, as well as cases of metabolic stress, and in convalescence.