Is there a specific word to describe the opposite of egotistical - acting for the specific benefit of someone else?

Perhaps this will fill the need;

al·tru·is·tic

/ˌaltro͞oˈistik/

adjective: altruistic

showing a disinterested and selfless concern for the well-being of others; unselfish. "it was an entirely altruistic act"

synonyms: unselfish, selfless, compassionate, kind, public-spirited; More charitable, benevolent, beneficent, philanthropic, humanitarian;

"the desire is to appear purely altruistic with no apparent expectation


Perhaps

empathetic (adj):

showing an ability to understand and share the feelings of another