Hi Shahbaz,
Second hand embarrassment means to become embarrassed because of someone elses actions.
Example: Fred missed the penalty kick, I felt a lot of second hand embarrassment for him.
Keeping in mind that from my experience people don't really use that term. I also can't seem to find a proper synonym for the phrase.
However you could use the word empathetic or empathy in the same way. It means to identify with the feelings of another person.
Fred missed the penalty kick, I felt very empathetic for him.
Hope I helped!