I get a terrible headache and neck spasms if I sleep on my belly. I had to train myself not to do it when my migraines got chronic. If for some reason, I roll onto my belly, I always wake up in pain.
I have trained myself to switch from a side sleeper to a back sleeper & it was the toughest thing to do! Why bother, right? Well, for the same reason you did, chronic migraines! If I move even just my head left or right it gets worse. If I am on my side it gets worse, but them I also throw up much more easily. I have found that on my back, propped up with pillows, is the most neutral position for me. I also figured the the lack of cleavage & facial wrinkles was a nice benefit - though not worth it by itself.
I was a back sleeper my whole life but during my second trimester of pregnancy I had to switch to sleeping on my side. Not only is it bad for the baby to sleep on your back, it's also uncomfortable. It was hard to get used to at first, but now at 32 weeks it feels natural. Don't know whether I'll go back to sleeping on back after baby is born or not.