All you have proved is that there are two different ways of knowing about a discharge of neurons (external observation and internal thought/feeling). You have not proved that a thought/feeling is identical with a discharge of neurons. How could they be identical, if the former is a means of knowing, and the latter the object of the knowing? It is like saying that the seeing of a ball, or the feeling of a ball, is identical to the ball itself. Let us test the logic of your example:
1. The feel of acid reflux is one way of knowing the physical phenomenon of acid reflux.
2. The feel of acid reflux is identical with the physical phenomenon of acid reflux. (This corresponds to the proposition that thought/feeling is identical to discharge of neurons.)
Therefore, by substitution:
3. The feel of acid reflux is one way of knowing the feel of acid reflux.
So premises (1) and (2) together lead to a tautology. But (1) is non-trivially true, so there must be something wrong with (2). Hence it must be wrong to claim that thought/feeling is identical to discharge of neurons.
Of course I did not prove that they are identical. And I did not claim to do any such thing. All I said is that they could be identical, and that your argument did not show that they were not identical. Mine was a minimal claim. One and the same thing can be known about in different ways, therefore, pointing out that we know about our own thoughts in one way, and we know about neural firings in a different way, is no reason to think that thoughts are not identical with neural firings. And was that not your argument? So, again, I did not claim that neural firing is identical with a thought. What I did was to refute your argument a neural firing could not be identical with a thought. Whether there is identity between thoughts and neural firings is, of course, something for science to prove. It is a scientific claim.