What's a simple, cheap treatment for my hand redness?

Hand redness. Hand redness can be from infections which usually require a physician visit since it would be painful with swelling. Mild skin redness can be lots of different things such as mild infections, inflammation, dryskin/eczema, reactions to meds/detergents. Try a gentle aveeno (oatmeal) cleanser, otc steroid cream with a thick emollient such as aquaphor if no change see a physician.