Your situation seems worse than me. Meanwhile, I did MRI scan of my brain just to be sure and it came out to be normal, so I have no idea of root cause of my migraine and being a man, can't blame to monthly cycles.
My current Topamx dose is 150mg and I am taking migraine preventive medication called as Flunarizine (Doubt its available in the US) and after quitting my job in Dec, my stress levels are super low, so my migraine frequency has reduced drastically but as and when the attack shows up, I have no alternative to Ibuprofen 400mg.
I did notice though when I was taking a course of Prednisolone, I had no migraine attack for a month, so I suspect that migraine has to do with some sort of inflammation.
I am also maintaining a journal of my migraine and now that I have moved to the US, I hope to find a neurologist that really listens to me and medicates me appropriately.