Take a peek at this link and see if it helps..
http://edis.ifas.ufl.edu/ps044
IMO, Tylan 50 injectible (can be injected or if you have to, you can also give orally) would be the best *if* this is some form of CRD (chronic respiratory disease). Whatever you try, I wouldn't give different...
Mycoplasma G. (which can cause swollen eyes like that) can be transmitted by wild birds. Could also be an eye infection of course. If it's mycoplasma, you can treat with antibiotics like Tylan or Denagard (tylan is at the feed store, denagard is mail order only afaik).
If an eye infection, you...
Chicken sinuses run around their eyes like that, so it's most likely a sinus infection - can be caused by coryza and mycoplasma, just off the top of my head. As the poster above me asked, any bad odor? sneezing?