I feel kind of "gross" when I eat fatty foods, though not as bad as your symptoms sound. I mostly feel "off" when I have excessively greasy foods (which I rarely eat). My stomach kind of feels uneasy and I may have digestive problems. I don't know if the grease doesn't sit right in my stomach or it something to do with not being used to it.
I really don't know if it's an allergy or maybe an allergy to something added to the grease or something completely different.. The only thing I could find was this article on gallstones:
Livestrong
Or did they already x-ray/test for gallstones?