Red-Eyed Tree Frog swollen chin?

[Kisa]

The eyelids not closing is fine, they have an inner eye lid that protects the eye while they sleep but also allows them to see their surroundings and check out predators. As far as I know anyway. Here's a pic I found online of one sleeping.

http://travel.mongabay.com/costa_ric..._rica_5850.JPG

That's normal. And for the first few months they may sleep with them open wider, maybe out of paranoia. My WTF slept with one eye open for two weeks after I brought him home.

As for the yawning, could they have been shedding?