Penicillin, yes. But also, check her nose and her ear. The ear may be difficult, because you have to push those tiny feathers aside to see in it. Is her nose clogged? Do you see a lot of gunk in the ear?
If so, try getting something called "VetRx" (if you're in the U.S.) and putting some drops in her nostrils and ears with an eyedropper. You may want to do this anyway with her nose, as it COULD be an upper respiratory infection and the inflammation is located right behind her eye. Chickens often display the symptoms of respiratory infections by goopy eyes, just as humans have watery eyes when they have allergies from pollen. It's all connected right there in our faces.
The VetRx is a camphor, menthol, and mineral oil combination. The oily part of it will help keep the mucus from gluing anything shut like that. It won't stop it, but it can help.
Aside from that, just keep cleaning the eye, keep giving her penicillin, and keep her as comfy as possible.