While trying to throw from a woodsy area the other day, I scratched my cornea because of a branch. I'm no doctor, but I have some advice. First off, wearing sunglasses is a good habit. If you don't like wearing them, keep a pair in your bag for shots from the woods.
I went to the emergency room with my injury, and they pretty much just gave me some antibiotics, a tetanus shot, and some pain pills. My eye still hurt just as bad for three days, until I went to an actual eye doctor. He corrected my problem almost immediately by giving me a "bandage," which was like a contact lens, that let my eye heal without my eyelid rubbing against it.