I have the exact same situation as you- I have to be on progesterone forms of birth control. I tried the mirena but now I'm on a progesterone only pill, (also called a mini-pill) ortho-micronor.
If your migraines get worse with this pill or are suddenly worse than usual, you need to see the doc right away.
Also know that progesterone only pills are much more picky about timing- if you are even an hour late it can be less effective, if you miss one, you're in trouble. Therefore it's a good idea to keep a plan b pack around, so if you have sex one night, miss the next pill, you have a backup plan. Know what I mean?
Your body shouldn't have too much trouble switching though, it's not that drastic. I hope your migraines get better!
Eiri- migraines with aura is when people get severe migraines along with visual side effects- for example, I get tunnel vision when I'm about to get a migraine, and then they're so debilitating that I need to stay in bed for the day or a few days. People with these kinds of migraines are at a much higher risk of blood clots/stroke when they're taking estrogen. So some doctors won't prescribe it for you (including any who were trained at planned parenthood!)
Tsukaira- you can pm me if you have any questions- I went through all this a few years ago and learned a lot about it!