Hey there -are your lips completely clean of any type of moisturizer during radiation? I had skin trouble on my chin and lips and kept moistuizer on during radiation treatments and made things so much worse - didn't even think about my chin being in the path of scattered radiation. When I realized what I was doing (after several weeks) I stopped and my lips and chin eased up quite a bit. Got a lecture from the radiation therapists too!
My lips got so swollen that they had to cut the lips out on my mask! Not sure if the solution for you is as easy (all things being relative during the hell of treatment) as it was for me- but I hope so.

I also tried a medicated lip balm by blistex which was cooling and a bit numbing - if you haven't tried it you might want to!
Good luck to you!