Tamara, My heart goes out to you to have so much to deal with. I have not had radiation, so I can't give a good answer to your question about the burning, but my nose is also affected by my position, and it does get extra dry because of my surgery in the area. I make regular use of saline nasal spray....non-medicated...and I recently purchased one called "Ayr" that had a bit of glycerine in it, to help coat the tissues longer. I liked it. I wouldn't presume to make any other suggestions, but I know that these two things couldn't do any harm and might make him a little more comfortable. With such a complicated medical situation, you should, it seems, run everything past your doctor before using it.
Good Luck. I know it is difficult for you to watch him be any more uncomfortable than is absolutely necessary!!
XO--Colleen