How can one address the problem of involuntarily glancing at others' 'awrah, which causes great embarrassment?

You must avert your gaze from what falls upon it, cut off thoughts about it, and strive against your soul to abandon it. Occupy your heart with the remembrance of Allah and feel His watchfulness over you, for persistent indulgence in such thoughts will lead to worse outcomes. Therefore, Allah commanded lowering the gaze, and looking is a form of zina (fornication/adultery) as the Prophet (peace be upon him) said. Rid yourself of this habit and strive against your soul, for whoever strives in obedience to Allah, Allah guides him to the paths of His reward.