Can you use neosporin in dog eyes?

I wouldn't recommend doing so - Neosporin is a triple antibiotic ointment or cream that includes at least one antibiotic that is extremely toxic when ingested. Since dogs are notorious for licking away every cream, lotion and goo placed on their skin, you would risk a serious medical reaction if you used Neosporin on a dog's skin.

The good news is, keeping the skin clean, dry and exposed to the atmosphere does a lot of good in clearing up rashes in dogs - simply clipping the hair close with a men's beard shaver and keeping the area dry can go a long ways towards resolving issues like hot spots.