I think this was posted a week or so ago, but since I have
experience with it (like many others here!) I wanted to also add a
note. I agree with you about the use of antibiotics. It "feels"
like doing something, and sometimes it does. There are signs to
look for to see if one of the common virii that causes URIs causes
a secondary bacterial infection (which is the only thing helped by
antibiotics) and a good vet can tell if a viral eye infection
progresses to a secondary bacterial one. With my latest two that
were constantly plagued by eye gooies and sneezies, I did like you,
and wiped their eyes with a cotton ball moistened with warm water.
Several times I brought them to see the vet but it was if the
appetite was deteriorating, and that is often due to stuffy nose
and inability to smell the food. Over the course of many vet visits
for these two, I was sold several different types of eye ointments.
Some with steroids, some without.  They can only have eye ointments
with steroids if there is no sign of an ulcer in the cornea. To
tell the truth, I never saw any relief from the eye stuff. The
thing that helped mine through the rough times was L-Lysine. It
helps to keep the virus cells from multiplying, and if started as
soon as symptoms are noticed, keeps it from getting really bad.  
Some cats need to have L-Lysine supplements their entire life.  My
cats seem to have finally outgrown it, or have built immunity, but
sometimes I still have to wipe their eyes. Also, ask your vet about
an antihistamine to help dry the nose to stop the sneezing. One of
mine would sneeze so frequently that he sneezed blood droplets.