For quick pain alleviation, put a cold, wet rag on the eye. This won't last, but what will is washing your eye out with milk. Get about a fluid ounce of milk (if you have a shot glass, fill that up). Whole milk works best, but 1% and 2% should also work. You can flush out your eyes with this milk. Rest the cup of milk on the bone at the base of you eye. Pour it on your eye and try to keep your eye open (hold it open if you can). This will be a bit messy, but it is worth it. If you don't feel comfortable washing your eye out in the shower. It won't be as effective, but it still works.
Next time, right after you are done cutting the peppers (or whatever else you do with them) wash your hands with olive oil. Olive oil will breakwash up the part of the pepper juice that makes it burn.