She tried to 'put on a brave face' [=she tried to appear brave or calm] despite the pain of the injury.
You can refuse to talk to her if you like, but you're just 'cutting off your nose to spite your face'.
They made it on time 'in spite of the fact' that they got a flat tire.
(..) But you'll be disfigured. Or put yourself out of your own misery. Come on. He cut off her nose. To spite her face. And he did it very recently. Listen... I've decided to stay on till this is done. One of two things'll happen. (..)1995 Se7en