Student or Learner
1) Dish-washing will make your hand rough.
2) Dish-washing will rough the skin of your hand.
3) Skin of hand will get rough from too much dish-washing.
scott, good morning.
(1) Probably, many writing teachers would advise you not to use the word "skin." When you say the word "hand," everybody knows that you are referring to the skin on your hands.
(2) Perhaps your three sentences could be combined into one sentence, something like: Unless you use gloves, dish washing can leave you with dry, rough hands.
Have a nice day!