Is it osteoarthritis or rheumatoid arthritis? FWIW I haven't heard of any link between lactose intolerance and joint pain, but of course it's still possible. I'm not at all a professional, but I could see some link with rheumatoid arthritis since it's based on your immune system and there could be some connection there? Not sure about osteoarthritis. Then again joint pain can also vary based on air pressure I think, so maybe it could also be a coincidence? In any case if leaving out mild cheddar helps with the pain, it doesn't really matter why, the important part is just that it helps.