You mention one app that has used almost 2 gigs, which we will assume is the highest single user, but what is your total usage?
Two things to note are; If you go into Settings>Connections>Data usage - you see a number at the top that shows how much data has been used in a given time frame. This time frame can be and should be adjusted to match your actual billing cycle. On the Data Usage screen open the Mobile Data Usage page. Then touch the gear icon and adjust the starting date to reflect when your billing cycle begins. By default this will likely be the 1st of every month but mine for example starts the 8th of each month.
The second thing is; If you are on a limited plan or you're rationing data from a limited plan to others on the plan use the Data Tools on this page to set a warning and a limit. At the warning limit the device will issue a notification that the data limit is approaching. If you also set the data limit you will have options for what the device should do when the limit is reached.
Using those two tools will help prevent overages.
In your statement you also say that "you" received a notification of data usage but then go on to say that you examined your GF's phone. This brings up other questions;
Are you two sharing a Data Plan?
Are you expecting to share this plan 50/50 or in some other percentage breakdown? I ask because when I was sharing a plan with my kids and their mom, I was the one away from home the most so I set limits on each device that reflected that difference. So I my limit was 75% of the data allowance and they split the remaining percentage. If your GF is rarely away from the house setting her warning, limit and action should reflect this difference.
I bring this up because my next question is; was this a notification form your carrier or from the device? The default device limit and warning is low. So you also want the actual limit to reflect your actual plan. These are internal readings and do not come from the carrier as the device has no way of knowing what your plan limit is and in fact when you look at this last page it has a similarly worded warning.
Additionally there is a setting available to set apps to use Mobile Data Only. You'll want to be sure this is off.
Let us know what you find.