Also, am I the only person who has problems dieting because sometimes, for causes yet to be identified, hunger can trigger a migraine?

It doesn't for me, but a quick Google suggests that blood sugar and migraines are at least somewhat related, though I'm fuzzy on the details of how. That might be (but might also not be) mechanism for hunger triggering your migraines. You should get a test kit and find out; if that is the reason, then you can design a diet which won't cause migraines, and measurements will help you do so.