Having had migraines myself for a few years (the attacks are significantly less common these days), I can help a little. There are medicinal treatments like periactin / cyproheptadine that are antihistamines, but have the side-intended-effect of reducing the frequency and intensity of migraines.
You can also get instant migraine treatment packs that work by dilating your blood vessels (most of the time, a migraine is caused by vasoconstriction, or the blood vessels in your brain compressing to increase pressure). These, in my experience, lessen but do not totally diminish the migraine's pain.
Aspirin or similar salicylate drugs can kill a migraine quite fast, though they can have some unusual side effects. Nausea is not uncommon, and in rare cases gastrointestinal bleeding. If you're young-ish, I'd advise you to steer clear of aspirin for treating all but the worst migraines - a simple paracetamol can kill the pain pretty well. Plus, too much Aspirin or salicylates can cause liver damage in some people (though you have to be taking it pretty regularly for this to happen).
Additionally, foods with flavonoids or nitrates have mild vasodilatory effects that can help with headaches or migraines. The best examples of these:
Beet and beetroot, kale, spinach. Personally, I haven't found much of an effect with these except from beetroot juice which is almost as bad as the migraine itself.