>>2066-Get an allergy test. Standard IgE, as well as IgG and IgA. US Biotek is decent. (Some controversy exists about the applicability of IgG and IgA reactivity testing, but long story short, it solved a lot of my problems. If nothing else, it's a good heuristic.)
-Make sure nothing is wrong with your jaw, teeth alignment, or facial nerves.
-If your diet is a bit on the subpar side, you'd know it. Refine it. Rule out typical triggers. Also, watch out for tomatoes and eggplant.
The above got rid of my migraines almost entirely. I still have things that come episodically and resemble silent migraines, but they're quite rare. It also worked for my father who'd had migraines much worse than me for most of his life, though given the shared environment and genetic makeup it's not too surprising a solution had that overlap.
Good luck. I'm sorry to say, but there are no good migraine solutions that I know of... SSRI / SSNRI / NRI use is common, but taking a mind altering medication constantly is hardly ideal. Triptans are terrible as well, at least in my experience. I only took them twice, and each time it made me feel more sick and did nothing for what I knew was to come. Though some people do have great luck with it.
Hope you can fix it without medication. It can be possible.