Barbara, I agree with the others, this sounds like lymphedema (swelling caused by lymph fluid). It is very common to have this after a neck dissection and/or radiation. The big clue is that it goes down during the day. Try elevating the head of your bed by placing boards under the mattress. Sometimes a few inches of height will help alot. Over time it will get better.

Radiation does not "come out" of your body. The kind of radiation we received is like light energy. It is there only when the machine is on. It passes into and through the body. The exception to this is if you have radiactive "seeds" placed into the tumor area. (brachytherapy) These seeds do emit radiation while they are present.