What settings do you have turned on? Push Mail, and Location Services can use quite a bit of data. And if your phone loses connectivity with your WiFi network at home, it will automatically shift to cellular data (if it is turned on).
http://support.apple.com/kb/HT4146 provides some guidance. Keep in mind that any applications that you run could also cause your data usage to increase.
Hope this helps
If your daughter has an Exchange email account that has gone awry it could be causing constant polling but that would also be running her battery down in short order. But even that would not have come close to 16GB.
The only way she would come close to that is downloading large files (think HD movies or TV shows), streaming lots of movies, or playing streaming video games with heavy graphics. You can check her iPhone under Video to see if she has a number of movies. If all of those are negative I would check back with Verizon and ask for a supervisor.