It took me a while to finally give up red meat, because I love it, but my body HATES it. I would get those terrible pains you describe. This happens when I eat too much dairy/cheese too.
Strangely enough, I can still eat Bison steak ... apparently a lot of people with red meat sensitivities still can. So whenever I'm REALLY craving it, I go to a restaurant that serves bison or I go to Whole Foods and make some myself. It is kind of funny, because I'm Native American ... so I guess it makes sense I can still eat bison? Haha.