"Up to date" may be very misleading. In the case of iTunes, it means your computer has the latest iTunes its operating system can handle. But if your operating system is too old, this is the source of your problem. You should instead tell us the version number, which should be 12.4.3.
If you have iTunes 12.4.3, then see this:
If iTunes doesn't recognize your iPhone, iPad, or iPod - Apple Support
And if that does not solve it, then recover your iPhone as described here. You may have to try to enter recovery mode more than once to succeed.
If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support