This is so frustrating for her, isn't it? It sounds normal, but still it's frustrating.
Some pain relievers can be effective, but some are not as good with bleeding issues as others. So you want to think about this. Also you mention that your daughter had no ibuprofen with her - does your school allow kids to carry their own meds? Double check on this because, on top of how lousy she feels, you don't want her getting into a issue for having any kind of drugs on her, even over the counter. She can probably access it through the nurse's office with parental permission or a doctor's note.
As one poster mentioned, there can be other things like PCOS or hormonal imbalances affecting periods. Make sure your pediatrician is fully equipped to handle this, and ask whether you need a gynecologist. I am reluctant to send teens through a whole bunch of tests with endocrinologists and so forth - it's expensive, usually involves more than a teen really needs to deal with, and it often yields nothing more than a big prescription and an over-reliance of medications. I am similarly reluctant to send someone to the "natural foods" aisle because there is so much in there that is untested and which can cause significant side effects - not everything is labeled correctly, you don't know where it's made, and a lot of "natural" things are terrible anyway (think snake venom, poison ivy, toadstools and bella donna!).
There are some terrific advances in anti-inflammation and cellular health - you've probably seen a lot about epigenetics on Dr. Oz, PBS, and the major news magazines. There is a natural peptide which has been through extensive clinical studies and has had over 60 published papers from various scientific and academic institutions. It can do wonders to restore proper cell functioning and stop a whole host of problems when the body "overreacts" to normal functioning, from hormonal issues to autoimmune problems. You have to be sure it's in a bioactive form that survives digestion. I only know of one company that has the rights to it and I know it's available in a capsule as well as in a women's formula that helps with all kinds of menstrual issues from PMS to bloating to heavy periods to menopausal symptoms like hot flashes and night sweats. So it's good for women of all ages. It's also safe because it's given to small children. It's worth considering.