We had a chicken last year with a closed eye, turned a bit goopy, then a smelly head and sneezing. We looked it up and found HORRIBLE diseases with just these symptoms. However, she just needed antibiotics and rest. No one else in our flock caught it.
What I learned:
1.) wash the eyes with saline solution from the pharmacy; in a bottle intended for use in eyes
2.) you can use neosporin ointment in an infected eye...it is neomyicin (sp?)
3.) Vet RX in nostrils and behind the ears (like perfume, but maybe dilute with warm water just a bit) and in their armpits (wing pits) helps alot of minor respiratory stuff. Drops in the water helps, too.
4.) Tylan 50 inject. is good for many respiratory illnesses. Wait until there is smell, swell, or goop (and rule out any physical causes, something in the eye)
5.) Keep a sad sicko hen separate in cat carrier in a dim, quiet place.
Good luck! We had a hen who had a strand of hay stuck way back in her eye....it was almost behind the eyeball. So, LOOK FOR THE PHYSICAL possibilities. Shine an LED flashlight around her eyeball and see if you spot anything alien, we found a spec and carefully (with VERY CLEAN HANDS) rubbed it forward, it turned out to be a long piece of straw (long for an eyeball). She had blinked it back and it drove her nuts.