>>5 sounds like a good temporary solution. You can go to hardware stores and find one that's roughly your size then adjust.
>>1 Try visiting a dermatologist. They specialise in things related to the skin. If it's a major discomfort I'd say it's worth a shot.
If you don't like the glove idea, maybe try coating your hands in something powdery like baby powder before dancing. But before dancing just test with someone/something if it has a bit of friction and you're able to grasp things or hands.