Eeeesh, both my phone and ipadpro say they are up to date w/15.7... no 16, nothing.
iPads won't get 16 until October. For Phones, did you look at the very bottom of the software update screen? A new major version is considered "optional" and they stick the upgrade to 16 at the very botom as an option. That way, you can keep upgrading 15.x, or chose to go to 16.