Immediately run your burned finger(s) under cool (not cold) water. This will stop the actual burning sensation and will soothe the affected area. Fill a bowl with cool water and rest your hand in it for ongoing relief. Look for any skin damage. A mild burn is characterized by red skin and sometimes small blisters. You can treat a mild burn at home. However, if you have a severe burn (large blistering, charred skin, peeling skin), seek medical attention immediately. Apply an over-the-counter, topical burn ointment to your burn. Cover your hands/fingers with a non-sticky bandage. This will minimize the chance for infection.