Not familiar with your ailment either, and adding Baking Soda a good idea. The reason for the burning is (probably) the acid iritating the bottom of the esophagus. Vitamin C is a weak acid, and it won't make your stomach more acidic.
You can get the benefit of ascorbic acid - without burning, bloating, gas or diarrhea. See http://www.livonlabs.com
Lypospheric C, but it is expensive.