I went through surgical menopause about 15 years ago and prior to that I had terrible migraines with all the symptoms you mentioned. I took estrogen for a few years after and, although the headaches eased up I still had them and then, all of a sudden, they stopped! It was wonderful! I went almost 10 years without a real "lay it down, dark room, throwing up, all day (or days)" migraine. Then I got sick and now I have them again.
The point of this is that yes, the headaches do react to hormones so when yours are out of whack the headaches decide to visit. The good news? It is possible for them to go away once menopause is over!