Got a vet? What kind of antibiotic spray are you talking about? Anything for eyes needs to be an opthalmic ointment. You can get an opthalmic antibiotic ointment at many farm and vet supply, usually some type of neosporin. It's somehing that should be in everyone's vet kit. Don't worry if it doesn't say poultry on it. It's the eye part that's important. Apply it with a clean Q-tip and never ever touch your applcator back to the tube. If you do, use it only for that bird, that incident and replace it.
I have had tht problem a couple times (runny, sticky eye) bit it always responded to the ointment. I find it occurs most commonly with very young birds who may get bedding, hay, or some other foreign object in the eye and it causes irritation. Never had one blinded. The bird must be panic-stricken! If you have help, get that eye rinsed out gently and inspect it with a magnifying glass and a good light for any injury or foreign matter. Remove it if you can. WEAR GLOVES, all of you! Thoroughly disinfect afterward with soap and water, maybe some bleach. You don't want an infection or to spread it. You've probably heard of pinkeye.
Can you isolate that one goose with oner or two of his sibs who is less agressive toward him? Hopefully the damage won't be permament. Do use the opthalmic ointment because it eases the irritation and may help any foreign object to make it's way out of the eye or at least soothe the eye if there is a scratch or damage to the eyelid or cornea until it heals naturally. The little guy probably needs to feel safe and I think if you can make him feel safe with you (and at least one other sib), he'll heal better and feel that you will protect him. In other words, spoil him and his sib. (Tough job, huh?) Just keep him in clean fresh towel every time you snuggle him (you know you will) and wash/disnfect it before using it again. It the damage is permanent, that will be an important factor in how well the little guy adjusts. Let us know how he does, ok?