I did have the same problem about water going down the wrong pipe. I did have improvement after I hacked up some gross phlegm and it looked like some type of skin/rubbery thing. My ENT said the throat is sheding the dead skin.
After about 5 week post it seemed I could drink and eat somewhat.

Let me know what the swallow therapist says and what the therapy is.

large lymph node Left Neck around May 22 2012
ENT June 6, did needle Biopsy - Negative
ENT CT scan July 9 - Negative
Remove lymph node July 26, DX - SSC - T1N2aM0
PET Aug 7, BOT
Aug 14, endoscopy, 1cm - clear margin HPV+
TX 33 IMRT - 6 Chemo - Taxol/Carboplatin
TX chemo 09/04/12 RAD 09/05/12