Ouch! 

The best way to heal a burn on the skin is with Vanilla Extract.  I kid you not.  I keep a large bottle of the stuff in the kitchen for burns on the hands due to cooking, etc.

 In the mouth, I'm not sure this would work, however.  Maybe if you swab a little on your palate?  (I think it has high alcohol content)...

 Have you tried something for mouth sores?  There is a product called Kanka which is for canker sores which numbs the area and provides a protective "seal" to the sore as it heals.  Maybe ther eis something similar for the paalate or for burns?

Good luck!