I think swallowing difficulties were one of my first sx's. i am undx'd at this time, but neuro 95% sure it's MS.
I know exactly what you are feeling with the cottonball thingy. I think what it is for me when I experience that is that my throat in that area is numb.
my other swallowing difficulties are when I have a really cold drink or eat meats and breads, then my esophagus will actually constrict and keep the food/drink from going down and it is very painful right in the middle of the chest. when this happens I sit back and up straight and just wait for it to subside, then the food slips right down like it's supposed to.
other swallowing problems for me are when I actually CANNOT make myself swallow my saliva - this is scarey for me. when it happens I will grab something to drink and that will kick in the swallowing motion.
you should definitely talk to your doctor about this. hope you can get past this sx.
God bless and best of luck,