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You can get an aversion to anything at any time. Over the next few days, keep a food diary and see what are your triggers and note the time after a meal. I am off and on meat all the time because I get similar symptoms like you. It also could be the quality of meat, how much fat the meat contains (fat takes a lot longer to break down and requires more bile in the stomach to help digest) if you don't have a gallbladder this can be a real issue. Now I have at least three meat free meals and if we have meat it's a very small portion.
If I have a large portion of meat at a meal I find I feel like I have a brick going through my system. Smaller portions are not a problem. I have 3 meat free meals a week, and my insides do feel better on those days.
A food diary is a very good idea. If you went to a naturopath they would ask you to do that anyway.
I have found as I have got older there are some things I cannot tolerate that I could eat a lot of when I was younger.
If I have spinach or silverbeet (both of which I adore), I get a bad attack of the runs the next day.
I have to limit myself to very small portions of pumpkin too, or disaster the next day.
Some people are allergic to something called "lectins", which are part of plants (not leptins, which are different).
I also have to drink A2 milk now. If I have a milkshake from a shop, I get a bad attack of diarrhea within 4 to 6 hours.
I have learnt my triggers through trial and error.
Do a food diary & elimination diet, start with basic foods and then add or remove food/groups to see how your body responds.
I had the same thing, turned out it was dairy intolerance and possibly gluten, first doc said no but then I went paleo (more cut out crap and very little bread/pasta) and felt so much better after!
Could be a meat allergy or intolerance? Try cutting red meat out for a few months and see how you feel?
Did they test you for coeliac disease?
Why do you assume meat is the cause? Intolerances to gluten or dairy are much more common. But before leaping to any conclusions or cutting out entire food groups you should see your GP and ask for a referral for an allergy test. Then you'll know for sure.