Ill looking leopard gecko (swollen eye/head and thin tail)?

I go over to my friends house and they have a leopard gecko in a corner about 2 or 1 foot off the ground right next to the kitchen, all the fumes, heat, and smells of teh kitchen obviously go to him. I looked at it and its recently in the process of shedding and it's head still hasn't shead completely and I also noticed that its right eye is pretty swollen and it looks like its head is pretty much swollen as well. Also his tail is also looking pretty skinny and the color of his skin is still solid but a bit dark. My friend asked me to help him because they heard it's pretty expensive to take exotic animals to the vet. I told them to feed them more and take better care of them and to also change there location. As for the swollen part… I'm a bit lost.