DAY, I can sure understand why you're worried! I think a good first step would be to consult your son's PCP. They can certainly run initial tests and it's possible that they might refer you to an endocrinologist...sounds at least possible that it could be something being manufactured (or NOT being manufactured) by the brain but not necessarily neurological. As I'm sure you know, some hormonal conditions can cause MS type sx and are very easy to correct. As for blood sugar and diabetes, an at home test does not really tell the story. It has to be a glucose test, done in a lab over a period of hours. You just drink something and then they take blood a few times over a period of a few hours. Boring, yes, but very non-invasive.
Is it possible that your son would be more receptive going this route instead of to yet another neurologist? I'm unclear as to why the ENT said there's something wrong with his brainstem. Did he do any tests?