How to gain my mother's trust back?

I'm in 6th Grade(I know kind of young to be using Facebook) &I want to gain my mothers trust back because I want to use Facebook. I don't really use my Facebook for anything else really but to contact my cousins who're thousands of miles away. I posted something really stupid, and now she won't trust me with it. So I'm not allowed. I tried convincing her with, if you take my Facebook away,you're taking away my only way of contacting my cousins,to which she replied "Who cares?" So I asked her to step into my shoes." What if you couldn't contact so and so?" And then she was silent, which I really thought had helped to get me my Facebook back. I am thinking of asking how to get her trust back. Do you think this'll work?