얼굴이 빨개지다 (eol-goo-ri bbal-ggae-ji-da) – (face) to blush/flush
This phrase can be used to describe embarrassment and anger, which are the two most common emotions and expressions.
For embarrassment, the context would most probably be more than enough. But if you would like, you could add 부끄러움으로 in front to emphasise that embarrassment/shyness is the main cause.
However, for anger, we should add 화가 나서 (to get angry so) in front so that it is clearer to the reader.
Anyway, just a fun fact: the 빨 in 빨개지다 (to turn red) comes from 빨갛다, which means red. 지다 means to change or to become. So there you have it.
아까 내 옆에 앉아 있던 남자가 너무 멋져서 내가 부끄러움으로 얼굴이 빨개졌어.
The guy who sat beside me just now was really cool so my face blushed with embarrassment.
우리 삼촌은 성을 잘내는 사람이라서 항상 하찮은 일도 화가 나서 얼굴이 빨개져요.
My uncle is a hot-tempered person so his face would always be flushed with anger over trivial matters.
그녀는 분명히 우리 정현을 좋아해. 증거를 대하자 그녀는 정현 곁에 있을 때마다 얼굴이 빨개지잖아.
She obviously likes Jeonghyeon. As proof of it, she would blush whenever she’s beside him.