'Connect to iTunes' after update iOS 9.2.1
When I connected my phone to my laptop today, iTunes informed me that iOS 9.2.1 was available. I tried to update it and put it away for a while, but when I came back, it showed the connect to iTunes screen. I force shut it down (pressed home and power button at the same time), and tried to 'update' it through iTunes as the Apple Support page said. However, it said that my iPhone 'could not be found'. What do I do? Do I actually have to restore it? Or is there a solution that lets me keep all my settings, pictures, etc.?
iPhone 5s, iOS 9.2, null