I have a friend who had severe problems with migraines. She had them almost daily. Now she has them about twice a year.
Homeopathy is much bigger here than in the USA, as it is in Europe. Her homeopathist sent her to an allergist and to a nutritionist. The allergist did a bloodtest for allergins and they found out that she was very allergic to gluten (mainly in wheat, which she loved), MSG, dogs, and to strawberries and some other food things. They tested a whole list of things.
Anyway, they put her on a strict allergy diet (very boring) and then introduced foods bit by bit over three months. They even tried the ones she was allergic to and she can eat them once in a while without any problem except the gluten and MSG. She also drinks eight large glasses of water a day and keeps a pitcher on her desk that she fills each morning with filtered water.
She not only lost her migraines, she lost a lot of weight and is now normal weight. That's what stimulated me to lose weight a few years ago by going on a fish and salad/green vegetables diet.
I don't really know much about all this but I know that she said her migraines had been caused by toxins and that she went through "detoxing" diets for a couple of days at a time when she first started. Whatever that means (I think its one of those terms that has lots of different meanings to different people). Anyway, she is happy, healthy and has never looked back. Once a very pudgy thing, she says she feels better and looks better than anytime in the last twenty years.