Here is my suggestion, keep talking to her in a way that is comforting, explain that every woman goes through some sort of issues with their period, make her feel like she is not the only one with this problem, you could even do some research on the internet with her and show her she is not the only one. Don't make her afraid of the doctor, and don't make her think that nothing belongs up there. I agree she is far too young to be thinking about boys or sex, but lets be realistic she is a woman (young lady) and even when we don't want to think about it, they all grow up, you did, I did, our mothers and sister ans aunts did. It happens, we just have to be supportive and understanding, tell her you too have been there, and know how she feels. As far as the heavy bleeding and cramping, I suggest Evening of Primrose, it is an herbal supplement, specifically for hormonal(female) cramps, headaches, bleeding. I take it one week prior to my period and the week of, ever since I started taking it,my periods are my regular, less painful and even shorter. And with this there are no side effects, and they are great for the headaches we sometimes get, I take it when I get stress headaches as well.
Just reassure her she is not alone, and give her the option of a female gynacologist, tell her if she goes, that the dr. might be able to give her something to ease her discomfort during her periods. Being 13 is hard, just remember how you felt, when you were 13, sometimes I think adults forget that we were once that age.