I've had two horses with corneal ulcers. The first was an older mare a number of years ago, and she was treated with the ointment as you're describing. It wasn't really helping, so the vet gave her another drug (probably like the one mentioned above that dilates the pupil), and sewed her eye shut for a couple of weeks. Of course she wore a fly mask when turned out, etc. Anyway, when he came to remove the stitches, the eye was almost completely healed, and there was only the tiniest of scars left that you could barely find even if you knew where to look.
The other case was not so good. We had a colt born here a couple of years ago that injured his eye at one week of age. It didn't look bad at first, and actually appeared to be above his eye where the skin was scraped up a bit. I cleaned it and all that, and felt sure it would be okay. By the next day, an ulcer had developed and I called the vet immediately. We started him on ointment and eye drops, but it wasn't doing much to help. He changed the drops after a few days, but that didn't help either, as it had developed into a "melting corneal ulcer". (The name of it still just about makes me gag.) Anyway, we weren't able to save the eye, and it was surgically removed at two weeks of age. The good news is that he lives a perfectly normal life with just one eye. The bad news is that we can't show him in AMHR shows with just one eye.
I sincerely hope the outcome will be much better for your mare, Julie. My best wishes are with you.