I know several people who have applied and received disability for migraines. I can tell you that it is a long and strenuous process and you need a good doctor on your side who can fill out some paperwork and knows your specific history.
The specific individuals that I know had other things that were involved with their migraine disease, such as depression, anxiety, fibromyalgia, restless leg syndrome, some people had even previously had strokes due to their migraines. (I have also)
I know that when you file for disability you should not be working at that time, they would figure...well, if you're working now...why should we award you with disability???
I have thought about filing...but I am young and I think my family has no understanding of what I go through or how I feel and that it would not be understood at all and let's say "frowned upon" to put it nicely. I was fired from my last job, a sales position for performance and attendance and I think if I were to file I would have my records from that place of employment included to show how often I missed and how at the beginning of my job there (before the migraines were as bad as they are now) I did not miss that often and I was at the top of my game.
Anyway, long story short...do some research on it, find out what you can...and in the meantime keep records of everything, so if you decide to do that you will have your "ammo"
Let me know how it goes or what you decide to do,