Are there any over-the-counter medicine for a minor eye infection?

Not really. There is no over the counter antibiotics for eye infection. You need to see a doctor. If its allergy or viral infection then one can get an artificial tears or allergy drops over the counter.
No. Any bacterial eye infections should be treated with a prescription antibiotic. Most viral infections do not have a good antiviral medication that is effective and you usually have to let them run their course (e.g. "pink eye"). Certain herpes infections of the eye can be treated with topical and/or oral antiviral agents.

Related Questions

I have an eye infection I ususally get when I am under a lot of stress. What is the over counter treatment you recommend?

Needs a look by MD. Stress may lower your resistance to infection but will not cause infection all by itself. If your eye gets red frequently, let an ophthalmologist look at it once to see if there is no other problem. He/she might recommend eyedrops to use to deal with the redness which probably is not an infection.