Could I develop burns from the radiation being used to kill my cancer?

Yes. Depending in where and how the radiation is done, skin reactions that are like a sunburn can happen. We have creams and lotions to treat these change and most are mild or moderate and heal quickly. Even terrible burns that are less likely will not need wound care or skin grafts as these are not 3rd degree burns.
Yes. Yes. It is more common for radiodermatitis (redness, tenderness, skin burn) to happen if the organ being treated is near the skin (for example breast). It is less common when the organ being treated is farther from the skin (for example prostate).