Could tmj joint pinch the nerves & blood vessels, preventing sweat glands on chin from secreting sweat and prevent nutrients to chin?

Highly unlikely: The tmj's are a completely separate and enclosed system from the chin area. The nerves associated with these joints are distinct and separate from nerves that control sweating. The skin around the chin may not have as many sweat glands per surface area as other parts of the body.

Not really: There is no anatomical basis to think that this could occur in my opinion.

Probably not: It is possible to impede nerves and blood flow, but what you are expressing sounds more like a neurologic problem than a TMJ problem. I would recommend you check with your dentist or ENT to have them do a work up and find why you are having the problems you express. It could even be trigeminal neuralgia, but seek competent help to find your answers.