I would get the Cipro drops that Casportpony recommends. I actually was looking for that medicine she had recommended on another thread. The eye ointment you have is the same as Neosporin plus a steroid anti-inflammatory. That could work, but the Cipro would be a better antibiotic. You could use the one while you are waiting on the other to come in the mail, I suppose. Be sure to flush the eye with saline first if it is gunky.
First State Vet Supply sells Cipro drops and one with a steroid. No prescription needed.
Thank you both for all of your help!! I'm crossing my fingers that this will do the trick!!