My 1st choice for major is Msc Social & Public Communication. However, I do not have either bachelor degree or professional experience of media/social science. My 1st degree is BA in Economics, and I've been working in marketing function for 4 years.
I wonder whether the admission will concern media background. If so, I would choose Health management (Economics) as the 1st major in the application...
Is there any one from the same or similar major that can help explain?
Since you can apply to two departments (at least as of two years ago), you should apply to your 1st choice, and save Health Management as a backup. I'd also advise you to apply earlier rather than later, since some departments will stop admitting students when they become full.
Concerning admissions, I did a degree in the Media and Communications department with no media background whatsoever. While each department will have different admission policies, if you can show a genuine interest in the field through your essay and recommendations, I think you'll have no problem. Also, your BA in Economics would be considered a degree in a social science :)