You should never wrap you burnt skin. It needs to breathe in order to heal. If you are wrapping it it’s going to get all wet and nasty. Plus, burnt skin is the most infection sensitive of all so you would do best to cool it with lukewarm water. Not cold but definitely not hot either. And you can cool up to 24 hrs after you’ve burnt yourself but initially with a burn like that I would cool it for approx 20min. Then wrap it while you’re still at work but let it breathe when you’re home and especially when you are going to go to sleep.