It's good that you've given him a healthy substrate. Cleaning his eye with warm water, just like you are, is the only option you have until the cause of the infection is diagnosed.
I know this isn't what you may want to hear, but many times a cavy shows upper respiratory infections with early symptoms of runny eye(s).
Even if it's just an eye infection - the ointment or drops necessary need to be filled by prescription. Anti-bacterials don't work on viral infections; fungal/parasites aren't usually effected by anti-virals or antibacterials.
http://www.coldal.org/cavie.htm#gp_medi This touches on the eye infection treatment.
Here is more detail about URI's http://www.guinealynx.com/eyes.html
Remember, early treatment can prevent it from turning into pneumonia or even something else. I truly wish you all the best with this special little piggie - he obviously means a lot to you.