Agreed with the above. Try applying to some jobs and see what happens. A lot of people at my institution in various roles have master's degrees, but not necessarily in higher education/student affairs. Like olympichopeful said, if you can get your foot in but there's no room for advancement, you might be able to enroll into a higher ed program at the institution you work at. If you can't get in anywhere, then you'll know to apply to full-time master's programs.
Also, I don't know if it's common but when I was beginning to research master's programs, I saw some places don't like those who already have master's in other disciplines to apply to their programs (they recommended applying to their corresponding Ed.D/PhD program instead).