When I got my chicks from Ideal, one had a closed eye. I thought it was just banged in transit, so I ignored it. The chick never got better. It wasn't really sick, so I didn't know what to do.
I tried Terramycin eye ointment, but it didn't cure it.
Then the chick started to sneeze...
I would not use an antibiotic on a chicken unless you have taken it to a vet and had a culture done.
Some chicken illnesses are fungal and antibiotics make them worse. Unless you know what you are dealing with, you may do the wrong thing.
Give her three drops of PolyViSol on her beak each...
Can you look down its throat and see if anything is stuck? I had problems with my chicks eating the shavings so I had to put them back on paper towels. It may have a pine shaving stuck in its throat or crop.