Any eye injury can be painful because nerves in the eye are damaged. An eye injury for an hamster can be painful. The injury may need professional medical attention depending on the degree of damage.

when Jeff got his "eye injury" the was facing edge and i cant remember when cm punk got his "eye injury" he was facing Jeff at the bash

Apply a bandage to both eyes.

Some object penetrated into the eye.

In medical terms, that would refer to an injury to the eye socket.