My hands hurt like that when its very cold - but I don't recall it ever being accompanied by nausea - on the other hand I've become quite nauseated by overheating when the surrounding atmosphere is chilly - especially if I warm up fast. Could you have warmed the rest of your body up too much, while trying to warm your hands?

As far as keeping your hand from hurting so bad. My winning combination has finally been, wool glove liners, full finger gloves and add hand warmers when its really cold.