I have used 2 different things that work.
One is an rememdy my mom used to use on me when I was a kid.
Epsom Salt in Ice Water
Pour some of the epsom salt in a large bowl with water dissolve add a
lot of ice. Take a clean towel soak in water lay towel on burn.
Towel will draw out heat, when towel is warm re soak in water, keep
doing this until towel does not get warm anymore. It always has
always worked on my kids and myself.
And we usually did not peel.
The other has been mentioned and that is vinegar, the one came from
my husbands side of the family and if he gets burned he uses the
vinegar. Just soak a towel in it and lays it on the burn.
Good luck
Diana