Why Would My 12 Year Old Cat's Right Eye Be Severely Swollen Shut?

It started just watering a lot, but now it is shut and she has rubbed it raw and bleeding trying to make it better. We're not abusive parents and she doesn't come in contact with small children. She is our only cat. She was taken to the vet when it started to swell and doctor prescribed antibiotic that hasn't helped at all.