It burns your hands because sometimes there's disinfectant in it: it means it's actually doing it job. Also, if you actually washed your hands regularly, it wouldn't hurt.
Soap is not a disinfectant. It cleans the natural oils off your hands and when it does this it is more effective than water alone, but not significantly more effective. Good hand washing technique is actually more important than using soap.
Also, I never wipe.