So sorry to hear about your digestive issues…miserable and dangerous.
I had some similar experiences, not being able to swallow, had gerd, hiatal hernia, swollen esophagus, etc etc.
First doc, seemed to have no clue and ordered no tests. I lost a lot of unnecessary weight, and started to loose focus. In desperation, I went to a privately owned supplement and vitamin store. Explained my situation and they recommended something that is made from a porcine enzyme (pig) product. Again, desperate…Well, after several days I was able to eat and not feel like something was stuck. Told doc about this product, and as he walked out of the room said there were better things than that. 😱 never shared that info…
Changed docs…
Second doc ordered 4 tests within 2 weeks, and found some things…and put me on a diet for CIBO.
Changed my life…you have to be completely diligent on the FODMAP diet, so read about this stuff. Lots of info online.
There is also an expensive med that might work in your situation, but still have to stick to the diet. If that is something you need.
Good luck and keep searching!!!

that is exactly what i am saying - there is no physical obstruction but you yourself said when you had the barium it is "backing up" and the manometry showed you have a motility issue. It is called esophageal achalasia. the regular GI docs i have found are not helpful with motility disorders. You need to find a specialty center that deals with it. - usually at a University hospital. where do you live - what state/city?