I personally have had no trouble with the swallowing mechanism, but used to get sporadic and very acute
pain immediately after
swallowing. To begin with this was always at the top of the
throat, right at the adam's apple, but later on I'd sometimes get acute pain at the very bottom of the esophagus.
My gastroenterologist diagnosed me with GERD and said I have an esophageal stricture, which causes a narrowing of the tube. She doesn't think all this is connected to MS, but I wonder.