My condolences. See my thread on "eye infection" for my tale of woe.
I had my kitty at the vet at the same time as another cat owner with exactly the same problem.
The vet puts eye drops in the eye (that's fun!) that show up under a black light, then looks at the eye with a black light while I hold the cat (that's fun!) to see if there are any scratches on the eye itself. There weren't in my case.
With no sniffling or sneezing, he ruled out the second probably cause: upper respiratory infection. He then chalked it up to just a plain old eye infection (conjunctivitis). Could be caused by a scratch from another kitty around the eye that then led to infection.
Anyway, the treatment is an antibiotic/bacitracin ointment in the eye three times a day. Now we are talking some serious fun!
Cost me $50 inc. the $15 for the eye ointment. The fun of trying to put ointment in a kitty's eye? Priceless.