I think this might be a great solution for OP. Somehow they don't die of the radiation (highly fictional), but their mutating cells (which does happen when exposed) do cause a glow that just isn't really a thing as OP describes it. Just gotta learn the basics of mutations as described by real Biology a bit and add some weird fictional protein/amino-acid that "turns on" and makes the fictional character glow, making it clear they have been exposed. So many places you could go to from that