By the sounds of it, John is just under-educated on your condition and genuinely is just trying to have a joke on with you.
Personally I wouldn't try and look for new jobs but try talking to John.
Pull him over for a chat again and say
Hey John, I don't know if you know but I have psoriasis which causes the look of dry skin. I don't mind when we joke on about other things but I get very self conscious over my condition. I would appreciate if you didn't comment on it or make jokes.
Repetition is the way that he's going to understand that you genuinely don't like it.
If this doesn't work or at least decrease the amount (will probably continue to decrease over time) then I would talk to your manager rather than quitting your job. Just because they're close doesn't mean that your manager won't talk to John about it.