The memory isn’t protected, so just like a hard drive in a computer, when you hit the limits of its storage, you risk overwriting data you rely on.
All you can do is back-up the phone as it is now, and then restore it from the previous back-up.
Depending on how long ago that was, you probably won’t have all the current text messages, etc, and emails may not re-download if they’re removed from the server.
Other than that, all you can do is lose some of the apps/music/videos you don’t use or are taking up too much space, and re-input your passwords, assuming you can remember them – there’s no magical recovery option leaving everything as it currently is.
Sync’ing phones is every bit as important (and should be done as regularly) as a home computer, and it takes no time at all to do so, even if using iTunes itself rather than over the air to the iCloud.