She was 'burning for' a chance to prove herself. [=she wanted very much to get a chance to prove herself]
('humorous') “We were talking about you last night.” “That explains why I 'felt my ears burning'.”
She was 'burning with' anger at his rudeness. [=she was very angry because of his rudeness]
(..) What kind of a man are you? You have sat here and voted guilty with everyone else because there are some baseball tickets burning a hole in your pocket. Now you have changed your vote because you say you're sick of all the talking? - Now, listen, buddy... - Who tells you that you have the right (..)1957 12 Angry Men