Rubbing human skin causes heat and friction.
The "burn" is an abrasion from the rubbing, which takes off the top layer of skin cells. It is not a thermal burn (such as with hot coffee). Magic erasers are not toys, and should not be used on skin. For an abrasion that's not oozing, some Hydrocortisone
1% cream may help. For one that's oozing a bit, some neosporin cream
or ointment may help.