DO NOT MESS AROUND WITH AN EYE!
Get a good equine Vet to look at it IN PERSON. The type of treatment required is exactly opposite for an eye with even a tiny scratch or abrasion as opposed to an inflamed or irritated eye from allergies, a blocked tear duct or ???
I would not let any Vet put a steroid drop or ointment in it without a thorough examination. I usually opt for dying it first to see for sure if there is even a tiny scratch or abrasion. I have known of horses losing sight in an eye when an antibiotic with a steroid in it like Gentocin Durafilm was used when a Vet just dispensed it across the counter and only asked the owner if the eye was scratched. I have also had horses (have one now) that is partially blind because of a bad Vet treatment.
A straight antibiotic ointment will not damage any eye, but will not clear up an inflamed one as quickly as a steroid + antibiotic ointment will. Sometimes, an injured or inflamed eye will not clear up in mid Summer without a patch or a fly mask that has been blacked out on that side.
So, please call a Vet and if it were my horse, I would not wait until Monday because eyes can go south or go blind very quickly and sometimes the damage is not reversible.