The location of your cut may have been the reason you nearly fainted. When I worked at the butcher shop, a coworker cut just the tip of her index finger off on a deli slicer. She got part of her nail, too. It bled like a bitch, and when I ran it under water, she passed out cold. I wonder if it's something to do with the nerve endings there?

Your choice of knife is probably the culprit. You should be using a broad-bladed knife to chop stuff. Do you have one? Lessons are free.