How to not use data on family plan with iphone 5?

I have a big problem, I have an AT&T iPhone 5 16 gigs with a family plan. I've been using it for a while. But the big thing is, It keeps crunching down my usage for my data plan. And I'm constantly charged by AT&T with annoying bills. I'm stuck with this data plan and the only way to get out of it is to quit AT&T. But it costs 300 bucks and I want to avoid that. I tried to cut off some apps using data like Facebook, Mail, and even tried to completely turn off my phone to avoid it. But still no use. My mom has an iPhone 4 and I can't trade sim cards because they are 2 different sim cards. I also asked them to switch our data plans so I can have the unlimited and she can have the 2GB data. But they said that they can't do it. Is there any other way to STOP ANY data usage? This is killing my Collage savings.

You need to figure out which apps are using high amounts of data. Uninstall All your apps then slowly add them back 1 every few days until you discover which are using all your data.