Frequent app and iOS 9.1 crashes

The rundown - iPhone 5S, bought new at its release (~15 months ago). iOS is 9.1 and iTunes is 12.3.1.23. MacBook Pro running 10.10.5.

In the past week, I've been having more and more frequent app and iOS crashes on my iPhone 5S. I've removed some of the offending apps and re-installed, but that's not fixing it. While driving and the phone is connected via bluetooth, the particular offender was Waze. Today I was driving and any app that is open (twitter, FB) will crash within a few minutes (goes to a black screen, then several seconds later goes to my home screen), and the bluetooth connection drops and a moment later gets reconnected. My phone is turned off / back on several times a week, so I don't believe that long uptime is an issue.

Fearing the worst case, I'm working to make a new backup via iTunes (the most frequent one was just a few days ago), and now I'm getting new errors -

iTunes cannot sync iPhone because of an internal error (paraphrasing, from memory)

iTunes cannot be synced because the connection to the iphone was reset

After these, I did another hard reset of my iPhone and tried a backup. I completed a backup within iTunes but now I'm getting sync errors - it's advising that an additional 9.25 GB is needed for all the contents of my iTunes library. I'm only syncing music (movies are sync'd to my iPad).

I could try a factory reset and then restore from today's backup -- but is that 100% guaranteed to restore everything, including photos?

Anything else I could check/try before doing this?