Will penicillin v potassium heal pink eye?

Rarely: Almost all pink eye is viral in origin. Penicillin v is a fine drug but effective only against bacteria. So only if you had a really rare pink eye from susceptible bacteria would this be effective. Your ophthalmologist can sort this out for you.

No: Taking a few leftover pills of penicillin isn't going to fix your pinkeye. Pinkeye is often viral & may self heal over time. The bacterial causes are treated with antibiotic eye drops that are formulated for that area of the body.