I would get to the vet. With eye infections, you really don't want to mess around. Especially if your dog has never had an eye infection and you don't know what to look for.
That said, you can give dogs over the counter Polysporin eye drops that you buy at the pharmacy (~$12 for a bottle). After Libby got her first eye infection, our vet told us that if the same looking thing ever happened again, to give her a round of these drops (2 drops, twice a day, for two weeks) and to only bring her in if it got worse, looked different, or was accompanied by other symptoms.
But still, if this is the first, I would buck up and go to the vet. Eyes are too important to mess around with.