I'm very sensitive to bright lights. I blame it on light blue eyes, but I'm not really sure that has any part in it.
Better than anything else I've ever purchased, I found a GOOD set of polarized sunglasses to be essential for comfort in bright sun. I use the brown tinted "driving" lenses, as they seem to be the most flexible between different intensities of light. I find myself wearing them sometimes after the sun has gone down but before it's completely dark. They're fabulous in rain and fog as well. They're about the same tint as the old 80's "BlueBlocker" junk glasses, but with real UV protection. The polarized filters are the real gravy though.
As to why blue light specifically hurts.. I had heard that blue light has a focal length that causes the eye to strain trying to bring it into focus. I made the mistake of buying a blue lightbulb years ago during my adolescence so as to provide a low intensity light source while I was suffering periodic migraines. It made them MUCH worse, and would instigate a headache (not a migraine, but BAD) in no time without any other symptoms.