Is his enclosure wet or humid? Humid doesn't equal wet and soggy.
Sounds like his skin is irritated by the excessive moisure or he got into something. I would put him on some newspaper or paper towels and get the humidity to around 50%. The eyecap will come off with the next shed, so don't worry about it.
I've had a few babies feel that way when they urinate(AND spill their water bowl) and sit in it until I come home. They get a lukewarm bath and wiped off with chlorhexidine(www.valleyvet.com). Don't need them getting urine scald or anything.
Oh and what did your vet say to change the temperatures to? They should be 92-94 warm side and 82-84 cool side, no night drop. If he's a baby, he shouldn't be going off-feed for any reason other than a shed(but even then, most of mine eat in full blue).