One of the most common causes of a salty or sour taste in the most is GERD.
This can persist even without heartburn or other more classic signs of
reflux. Anti-acid medications like Nexium may not help - in fact they may
even increase the problem by suppressing stomach acid and allowing bile
salts to precipitate in the stomach, and those salts are still definitely
available to reflux into the mouth. Non-acid reflux occurs in 25% - 40% of
GERD patients and there are no medications to control it.

To nail that diagnosis down further a complete medical history needs to be
done. You should indeed raise the issue with your doctor, perhaps even go
ahead with the ENT appointment, but ignorance about the finer aspects of
GERD is common, and the concept of non-acid reflux is not one your typical
FP or ENT is likely to be familiar with. An alarming number of
gastroenterologists are woefully ignorant of the subject as well, but they
or someone well-versed in esophageal disease would be the most likely to be
familiar.

Ambulatory pH testing is the method by which GERD is confirmed, but standard
pH testing by either catheter or Bravo methods won't diagnose non-acid
reflux since it is alkaline not acid. It can only be accurately diagnosed by
MII (multi-channel intraluminal impedance) testing.

HMc