ios10 problems
touchscreen locks up and stops working during messaging and email typing.
iPhone 6, iOS 10
There are several things you can try if you haven't already. First (and easiest) is a restart and/or forced restart:
Restart your iPhone, iPad, or iPod touch - Apple Support
Next (and more drastic) would be a restore from backup and then restore as new:
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support