I agree, caffiene is the one ingredient there I'd worry about
. That usually upsets my gut. I get migraines that last days too, and often get rebound migraines. I take Maxalt and have never had any issue with it affecting my UC. It's one of the few migraine meds that doesn't actually say in the literature 'do not take this medicine if you have Ulcerative Colitis' (yes, some actually flat out say that! Imitrex is one that comes to mind).
However, I do often drink some iced tea after a migraine goes away just to prevent a rebound migraine. I do it only for a day though.