My friend used to have terrible IBS. If she ate anything greasy or any fatty meats, she would immediately mad dash to the bathroom. I introduced her to the grain-free lifestyle about a year and a half ago. She was originally very, very skeptical, but after seeing me undergo huge changes in my overall health and body composition, she determined on her own there was something to this and gave it a try. She's mostly primal out of habit by now and has been avoiding gluten for months. She can now eat fatty meat and greasy things no problem. In her case, she clearly had an autoimmune condition (likely due to gluten intolerance) where greasy meat was the trigger, but it wasn't the underlying cause.
I've never heard of a "pork allergy." Is it possible? I don't know, but if you can eat one kind of pork but not another, I doubt it's an allergy. You may have an autoimmune condition like my friend where something in pork is the trigger. Whatever your situation, it's certainly strange to me.
I also know people that have big issues with the texture of animal fat. If you give someone a pork chop or a ribeye steak where fat is in big chunks, it makes them sick. However, if you take that same meat and grind it up and make sausage out of the pork chops or ground beef out of the ribeye, even though the fat content is the same, the homogenization removes the fat pockets and distributes the fat evenly, removing the fatty texture. Perhaps you're grossed out by large chunks of hard animal fat, which pork chops and bacon would be rich in, but sausage would eliminate. It could be a mental thing, similar to how a vegan or vegetarian will vomit if they're told they've eaten meat without their knowledge.