If you do put ice on it, make sure the ice is wrapped in a cloth. I was scolded once at an Urgent Care Center when I came in with a plastic bag of ice sitting directly on where I had burned my hand. They were nice about it, but told me that the ice sitting directly on my skin could do as much damage as the burn.
Well if you burned your whole hand, but it in a bucket of ice or cold water, yes i know it will be freezing but it helps. If it s a simple burn, just get an ice pack. Yellow Mustard and Aloe Vera help cool the burn.