"keep your spirit up!" = 기운내!
You are right. Hwaiting (파이팅) is the English word "fighting".
We shout this when we cheer somebody or our favorite team in a sport games or enhance the mood at a party. Some Koreans point out that it is Konglish (broken English) and it should be "go for it".
But, in fact, Hwaiting became a too popular slogan in Korean society no matter whether it originated from English and so I don't think there will come up a substitute for hwaiting in the near future.