1
general::
Suffer embarrassment or shame; also, exert oneself to the utmost. For example, He was red in the face from all of the mistakes he made while announcing the winners' names, or You can try until you're red in the face, but you still won't get straight A's. The phrase red face was already used in the late 1300s to refer to blushing on account of shame. However, the interjection Is my face red! meaning "I am very embarrassed or ashamed," dates only from about 1930.
American Heritage Idioms
2
general::
Phrase(s): red in the face
Fig. embarrassed. • After we found Ann hiding in the closet, she became red in the face. • The speaker kept making errors and became red in the face.
McGrawhill's American Idioms And Phrasal Verbs