On the other hand I absolutely cannot eat red meat at all without serious GI distress.
Do you have an allergy to meat or an intolerance to it? My understanding is that an allergy involves an immune response, whereas an intolerance typically involves what could be described as a food poisoning-like response.
ETA about the 3+ reactions to foods you eat: that is really interesting. What did your doctor say? Is that common?
It's VERY common.
As many as 50% of positive skin-prick tests to foods are
not clinically relevant and have no real meaning in terms of being allergic to the food. NEGATIVE results in skin prick testing (properly validated with both +- controls) are about 95% accurate for foods.
RAST testing for allergen-specific IgE is also problematic, though there are some well-established positive-predictive values that define a good solid 95% confidence level. Above that, it's very likely to be a real allergy. But there are also individuals who have quite low levels of circulating IgE and still mount impressive anaphylactic reactions to those allergens.
It is quite individual, and even then can be pretty idiosyncratic.
