This is yet another database entry from personal experience, that someone could find useful at some point. Also, if you're a guy, the basis for the following instructions also applies for when taking a piss and forgetting to wash your hands before going(also from experience). Both situations hurt like hell.
So I accidentally scratched my nose before washing my hands after chopping up a cayenne pepper, i started feeling the burn but tried to ignore it. Blowing my nose, since it was running like crazy, didn't do anything to help the burn. So I brought my knowledge of oily substances to the test. Using vegetable oil, I soaked one end of a q-tip in the oil, and swabbed both nostrils and sucked in really hard. Did this about 2 times, and let it sit. A couple mins later, no more burn,