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]
(..) When you're hurt and scared for so long... ... and the hate starts to change the world. Alessa's hate grew and grew, burning inside her. ... she even hurt someone who was only curious. I promised they would all fall into her darkest dream. Don't be afraid. (..)2006 Silent Hill
(..) Oh, my God. You could be her twin. Are you Alessa? Where's my Sharon? Look at me. I'm burning. Rose? Rose? My God. - How did you get over there? - Where is she? Grab onto it. (..)2006 Silent Hill