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]
(..) were critically injured, but many of the wounded were also keen to share their stories. and next thing I know, is a loud, um, large flash of light. Uh, I felt a burning sensation on my hands, put my hands up to my face... Yeah, I can't recall anything prior to that anymore. Any noise, any bang... (..)2012 Zero Dark Thirty