When my husband finished with his 35 sessions of radiation, his epiglottis was swollen even att the 12th week mark. We were told that if he had forced down a box of Ensure, he would have drowned. In fact, what happened was that whatever he tried to get down (in teaspoonfuls) would come back up after a couple of days. The RO prescribed gabapantin which helped a bit with the swelling. The most important thing, I would say, is patience and wait for the swelling to subside.

For the thick mucous, you can use a waterpik with warm water, a bit of magic mouthwash, the tongue scraper supplied, and put it on the lowest setting. It gets rid of the thick mucous quite effectively and makes your mouth feel fresh. It's a technique I picked up from this forum way back.

Hang in there, you will get through it. It can be frustrating at times but the discomfort does end.