Is it possible to complete a Master's degree while working full-time?
A lot of people in the US do this, actually. Some places have enough evening classes at the MS/MA level that it may not disrupt normal work hours. But it takes a lot out of the rest of your life, of course. 

It is easier in a field in which you can complete the degree without research, say by coursework and/or creative writing. 

But if you can afford to spend three hours a night in class for a couple of nights a week and also do the required other work then it can happen on a reasonable time scale. And NYC has a lot of options.