Ghost shrimp is often a catch all phrase for shrimp that are transparent. So that means many species fall under that term.
The majority of "ghost shrimp" are not able to have babies that live in freshwater.
It is possible you received a red claw shrimp. I have them myself and love them as they grow bigger than 2" and are much more fun/active to watch than my dwarfs, however they do need a species tank of their own. Think of them like crayfish.