What do you suggest if my wrist keeps clicking - is this related to autoimmune uveitis?

Maybe: It could be, but there are so many things that can cause a wrist click that you cannot assume there is a connection without further evaluation. It could be osteoarthritis, it could be a tendon or ligament problem, a subluxation of partial dislocation of the joint (although those usually hurt). I would see your doctor for further evaluation.