Your first answer is what I wanted because quite frankly the first thing that came to mind upon reading your question is esophageal pathology. Pain is rarely a cancer compliant
early on so infection, erosions or ulcers is most common. The reason the Biaxin gave you some relief lead me more to an infectious etiology. Diabetes puts you at risk for opportunistic infections.
Neurontin is not normal medicine for diabetes. So I hope you have some neuropathy to justify its use.
The heart scan is not a cat scan of the chest. Pain with swallowing is either neck or chest pathology. A scope can see the inner lumen but the cat scan can see all structures and their surroundings. Unless they also read the heart scan as if it was a chest CT then you did not get what I think you need. MRI is also a good option.
The appendectomy is not an issue.
I am worried that the GI doctor has dismissed you because that discipline hold a significant key here?! Rescope is often needed and probably should be done. Biopsies !!! Wow these need to be done. Especially for H pylori, what if you have a resistant strain or you need treatment longer than the usual 14 days? Endoscopy could help. How about increasing the dose of nexium? Many times I find standard doses with this class of drug is insufficient.
A cat scan could evaluate neck structures & your mediastinum ( around the heart).
Now I will add this warning ---> As a surgeon I have had to chase the complaint for several months before the cause actually grew big enough to see.
I am not sure what else to tell you?! You need your doctors ( a doctor) to step up....