Why does your leopard gecko have a swollen eye?

He/She probably hit it on something or has a infection. either way you need to get him to a reptile vet (or 'herp vet' as it is normally called in the breeder and keeper world) as soon as possible. for now the best you can do is make sure it doesnt get worse and that he is eating and drinking.

Hi i have a leopard gecko and if it has something in its eye then go to the store or drug store and get some 0.9% sodium chloride irrigation,usp and a seringe and flush the eye out with it daily but do not touch the eye with the seringe.