My 16 gig phone is constantly low on storage, though all I can see in manage storage is <2 gig of music, mail, photos and apps.

Open iTunes on your computer, and connect your device to your computer. In iTunes, select your device. You'll see a bar that shows how much storage your iOS content uses, divided by content type. Hover your mouse over a content type, like Other or Apps, to find more information. If the storage still isn't matching up, then backup the phone through iTunes or iCloud, wipe the phone back to factory settings, and restore your information. That should clear out any phantom data that's taking up room on the device.

Check your storage on your iPhone, iPad, and iPod touch - Apple Support

What if you can't use iTunes, my computer won't use it, and can I just backup without it? And yes when some say it shows they have more storage on there then the phone says, what do you do then??