It doesnt appear to be reddened or swollen in any way... just wet as you say. You could try to find some eye drops maybe- but I dont know if it would have any effect- She how she is in another day after having the deeper water to dunk her head in... After having a swim - does it dry up and...
Swimming every day is a good idea when they dont have deep water in the brooder... they can make too much mess in there given the chance. Mine dont have water deep enough all the time- By the time I get home form work most of the waterers are empty - so I make sure they do swim every night...
Does she have access to water deep enough to clean her face in?? She may have a tiny spec of foreign material trapped under an eyelid causing her some irritation.