I am benching right now trying to do a PR. Even in warm ups with 135 my hand hurts.

Right now I am powering through it. Hurts like hell, but still benching. Will I be okay?

stop benching in full wrist extension. you hold the bar on your thenar and hypothenar eminences, not with your fingers

Dope. I don't have pain like op does, but I occasionally do fell a little pull when benching and was always curious. Makes perfect sense.

finger, wrist, or palm?

You don't notice it while benching, but if you took a video your wrist is most likely bent backwards, focus on making your wrist into a straight up and down line and the pain will go away. Wrist wraps will help with this if you put them on properly (wrap em tight till it hurts almost)