汗颜 is literary and modest — used to express your own embarrassment (rarely to describe someone else's), often when receiving praise or comparing yourself unfavorably. Common pattern:
令我汗颜 ('makes me blush with shame') or
自愧不如，
汗颜不已 ('feeling outclassed and ashamed without end'). The image is sweat (
汗) on the face (
颜).
