You might be on the right track with having GERD, if you are having feeling of the acid burning as well. GERD can make the throat look red. GERD can give sore throat (personal experience). I think dry air with forced heating can too in the winter.
But I don't think GERD normally affects the voice? And w/the lump feeling and redness, I'd recommend getting a second doctor opinion from another ear, nose, and throat specialist on this. You wouldn't want to miss if it were cancer or something.
Burping can be a sign of a gallbladder issue, I believe, also, so you might want to get that checked too.