As long as I’m here, first aid for a first or second degree burn is immediate cold running water on the affected area. This provides some pain relief and stops the progress of the burn. Don’t ice it, you may do further damage if you’re not careful.
Remove watches, rings, tight clothing, etc. from the burned area as well since there will probably be some degree of swelling and you don’t want those items to constrict anything.
Use your best judgement to determine when to stop the flow of water over the burn. Can’t stay tethered to the sink forever. Cover the injury with a dry, sterile non-linting dressing and bandage loosely. The intent is to reduce likelihood of infection since that skin is damaged and less capable of protecting itself but you still don’t want to constrict the area.
Consider the need for further medical attention, particularly for burns involving the face, hands, feet, genitalia, around joints or if they cover more than 9% of your body. You can use the size of your hand as a measuring tool as it will cover roughly 1% of your body’s surface area.
Do not apply mustard, vinegar, butter or other supposed “home remedies” as they may introduce pathogens that can lead to infection, damage the skin further or simply cause needless pain.