There are two different possibilities that might be causing this problem. The first, and most obvious, is that the gastroesophageal reflux disease (GERD) is the problem. There may be times when the acid reflux comes back causing your “burny mouth and throat” to come and go. The fact that the asthma disappeared may make it less likely, but it is still worth some investigation.
The second cause is that the throat inflammation is coming from your upper airways, especially your sinuses. It is possible that there is chronic sinus inflammation also called sinusitis. This could be due to an allergy, an infection or ongoing exposure to an irritant, such as pollution or smoke. Sinusitis can cause increased mucus production. The mucus can drain from the nose and sinuses down the back of the throat causing a constant or intermittent postnasal drip, which is irritating to the throat. This is easier to evaluate than GERD. It simply takes a CT scan of the sinuses. Either it will be positive or negative. If it is positive, then further investigation will be needed to find the cause and control it.