Will a cat eye infection eventually resolve on its own?

That's a tricky question because I'd usually say that you shouldn't depend on that, don't wait, hoping that will happen. But cats are trickier than dogs because they can commonly have recurrent issues from a chronic herpes viral infection from when they were snotty-nosed, crusty-eyed little kittens. Herpes is forever, so it's still going to be around. Some cats can have flare-ups related to stress or changes in the household. I have seen situations where a cat may have a flare-up, and in some cases, its body deals with it, and it goes away. But you don't want to be wrong when it could have gotten a scratch on the eye or the herpes flare-up led to something more that led to an ulcer or a scratch on the eye. So, don't wait for that to happen, have it checked out. You can't always see a scratch on their eye. It's not an obvious gash going across it. Sometimes it's a small area on the part of the eye that you can't see, and it takes special stains to show up.