All NSAIDs are anti-inflammatory. I'm kind of in the same pickle as you are, because I can't take Tylenol myself, since it makes me feel sick. And, I'm allergic to all opiates.
One idea I have, but please check with your GI first, is see if you can take an herb called boswellia. It shouldn't upset your colon, because I've taken it before without feeling any digestive issues at all.