Welcome to BYC.
I don't see any swelling in the photo, just some minor discharge in the corner of her eye, and the obvious closure of the eye.
How does the other eye look? Does she seem to be acting normal? Is she eating and drinking ok? Any other symptoms we should be concerned about, sneezing, nasal discharge, rattled breathing, etc?
Basing off the photo, it looks like there might be some dried blood on her eyelid, so she may very well have gotten pecked and it's now sore. A lack of other symptoms would support this theory.
I would try flushing her eye with some saline, or eyewash, wiping off any gunk with a damp towel, then applying either an antibacterial ointment like Neosporin or an ophthalmic ointment like Terramycin to the eye, repeat as needed.
I personally would avoid administering tylan intramuscularly since it often causes muscle site necrosis, and just as a further note, you need a prescription to obtain Tylan 50 therefore it's not available at feed stores.