Why do my armpits itch and burn after shaving? And what can I do about the itch and the burn.

Injury. Shaving is associated with some degree of injury to your skin. It may be minute but still present. Your skin may be too sensitive to even minor one. Sometimes, it is the razor you use or/and the shaving cream you utilize. Look into changing one or both of those. Also, after shaving, put a cool compress to sooth the skin. Using deodorant right after shaving may also cause irritation and burning.