2014 we dealt with Pink eye. Tried all sorts of treatments and the one that worked is Terramycin Ointment. Its Oxytetracyline for the eye. I wont be looking elsewhere for treatment options again. But feel free to check out the suggestions below for what might work best for you.
Recomended treatments for pinkeye: For a minor case try triple antibiotic ointment directly on the eye. NFZ Pink Eye Puffer put directly on the eye. You can find this at Jeffers
For a more major case squirt the eye its self with Penicillian or LA 200, enough to coat the eye, about 1cc Also give injection of LA 200 Human pinkeye drops are great!
Becareful when handling a goat with pinkeye. It can spred to humans and other goats easily. Thankfully none of my other goats got pinkeye when Destiny did. A good practice if you are able to do it is to separate the infected goat from the rest of the herd. Pinkeye is not fatal.