When I look at the storage section of my phone, the various categories add up to about 2.5 GB of storage, but it says that 11.4 GB is being used. Is there any way to figure out what else is taking up space on my phone?
Since the upgrade to iOS 9.2, I have noticed that my backup size has been growing by 100MBs with every sync. No amount of health data, mail or messaging can account for this. I believe it has something to do with the feature in iOS 9 which allows documents and data from applications to be backed up to iCloud Drive outside of the iPhone backup menu.
This "helpful" feature to iOS appears to store the documents and data accumulated by an app not only in the iPhone's local storage but also in your iCloud quota even though it is not transparent that it is doing so. Since for many apps, this local cache is many times larger than the application files themselves, it is possible that this is responsible for the rapid, undocumented, and unconfigured consumption of iCloud quotas.
Settings > General > Storage & iCloud Usage > Storage > Manage Storage > [any app]
Settings > General > Storage & iCloud Usage > iCloud > Manage Storage > This iPhone > Backup Options > [any app]
Settings > iCloud > iCloud Drive > On
Unfortunately, I have tried to delete and reinstall the most nefarious offenders and even though it has opened up over 2GB on my local storage and turned iCloud Drive off, the iPhone backup process has yet to recognize this adjustment. I do not know if this is a problem with the iCloud/iPhone negotiation process, or corrupted settings on my phone. But, this feature is the only feature that I have found that even comes close to adding up the 'missing' amount of data which is hogging up my quota.
Please check out What is other on iPhone Storage to get a nice way in finding your hidden storage waste.
Also to give you a nice way to fix this. Restore your iPhone to the most recent version and then place the backup file back. Don't just update as it won't remove anything.
Also check out this Apple KB about the space issue.
To summarize Apple's solution: