How to back-up specific apps and information from iTunes?

I had a 64g iphone 6 that had a hardware problem and could not turn on because it froze mid-way in the restoration process. As a result, I turned it in to upgrade to a 6s with a program my phone company has. Being in the financial difficulty I m currently in all I could afford was the 16g iphone 6s. I know I can t back up everything but there are some apps like my password protector app and a bunch of important, sentimental notes from my old 64g phone that I need.
It has to be through iTunes because I only backed it up through iTunes. I stopped using iCloud because of that glitch in the upgrade where you had to pay for storage a while back.

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