I'm sure you are OK if he is getting steroids. Be sure to continue the steroids an appropriate length of time. If you discontinue too soon, symptoms will recur. Sometimes you have to taper, restart, and taper again if the symptoms got well established and are hard to treat. Good luck with your baby. I know you must have been scared.
If antibiotic ointment doesn't clear up the eyes within 24 hours, I would jump immediately to suspect strangles. Hopefully there will be no long term damage!