The armpit sits on a big joint between your arm and your shoulder, so it does have some tendons, ligaments etc. there a big one that I can feel in particular on the outside of it, on the side of your chest. I've also just checked and yes, my armpits get a lot stiffer when I'm holding my arms up. Is there anything I particular you're worried you might have? It really, really sounds like nothing at all is wrong!