Something similar happened to my daughter, who is now 28, when she was 14.  She basically missed 3 1/2 years of high school. We worked with a local nationally-renowned headache clinic, went through 100+ medications, hospitalization, and finally sent home with a "we can't help you but you'll be in our next journal article"! Finally, I took my father's recommendation to try feverfew.  I'm  not a fan of herbals, but we had tried everything else and were desperate.  Amazingly, it had a tremendous affect on her headache.  We were careful to get a brand that guarantees purity and consistency of the central compound in the feverfew.  She continued to take it and recommend it to fellow sufferers, but discontinued it with pregnancy.  EVERYONE she recommended it to found it helpful. It is now harder to find, at least in my area.

Later, we talked to a dental specialist, who noticed that her teeth were ground down.  She grinds her teeth in her sleep, and he indicated that where he was trained in the UK bruxism is recognized to produce much of the same pain she was suffering.  Solution? a simple mouth guard.

Good luck to you.  Something like this affects the whole family.  You as a parent particularly suffer from the inability to make it better for your child.  It sounds like you're a good advocate for your child with medical professionals.  Don't underestimate the usefulness of a headache diary as you go through this process.  I once read a clinical journal that compared triggers with grains of sand added to a dune - they accumulate, until finally one sets off the landslide.  The takeaway is that your daughter may have many triggers and they are hard to distinguish because it's not always the same one that triggers that landslide.  It's a very complex problem.  For my daughter it's hormones (hers, mine, and her sister's - pheromones), weather, inconsistent food/sleep patterns, and avoiding some TVs and monitors.  And we got custom made sunglasses that were double tinted to be as dark as possible, as direct sunlight was another trigger.  As you find triggers through the diary, tackle each.

Another suggestion if the above doesn't work.  As I mentioned, my daughter suffered for a very long time, and her continuous migraine rendered her almost helpless.  This is something to beware of as it can influence future behavior as the sufferer becomes used to everything being out of her control.  Which means be a meanie and keep up with the discipline (which is hard when your child is suffering) and search out ways to put control back in her life.  Something as simple as choosing a movie (if watching doesn't trigger extra pain) or for my daughter, getting her her driver's license.  That took going through the school superintendent to get an exemption to attendance/grade requirements in my state, but the sense of control she got back was quite valuable.

Best of luck!