Yes, steroids will inhibit the healing process, but they are 100% necessary to control inflammation when there has been some sort of trauma to the eye. The abrasion will still heal even with the steroid being applied. If it's just an abrasion, the steroid can be applied right away when starting the antibiotic. If it is already an ulcer, you might want to do only antibiotic therapy (with a huge loading dose, round the clock) for the first 24 to 48 hours and then add the steroid. This is why a vet should look at the eye, instead of us just guessing. Sure, you can see a certain chunk missing, but instilling fluorescein dye (like the picture above) will show the true extent of the abrasion.
Resolved? No it's not. Just because you're starting an antibiotic treatment does not mean you are out of the woods. What did your horse get scratched on? You have no idea. It might have been vegetative matter, and your horse could be at risk for a fungal infection. If that happens, you do NOT want to put a steroid on it (one exception for steroid use) and antibiotics will do nothing to treat the fungal infection. Fungal infections are typically much more difficult to control than bacterial.
You are taking this way too lightly for the possible complications that could occur.
I know that life happens and things happen, but this is precisely why you should always have emergency cash for your horse (and for yourself) when emergencies health issues happen where it is in your horse's best interest to be seen by an equine vet.
To possibly convey the seriousness of the situation to you, when I have a patient that has an abrasion, I am definitely following up with them every day or every couple days, depending on the size and severity. An ulcer? I am seeing them in my office every single day until there is epithelium over the ulcer, and then every couple days until we see progress. Sure, more serious when we are dealing with a human than a horse, but the corneal layers are similar in both species and the risk is still great.
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It is not enough to know how to ride; one must know how to fall.