iPhone 5S touchscreen become unresponsive, how to properly calibrate it?
I would suggest taking a full encrypted backup of the phone using iTunes. Then restore the phone with the latest iOS without restoring your backup.

If the problem with the touchscreen freezes persist, you most probably have a hardware error (or at least an error that is not user-fixable). If so, you'll have to take it in for repairs.

If the problem with the touchscreen disappears, the problem could be a corruption in the settings in your backup. If you can do without restoring the backup, that would be ideal - otherwise you'll have to use third party utils to pick and choose stuff from the backup and copy them to the device again.