When I go to update to iOS 16 there is nothing all it says is iOS 15.7 is installed

Have you ever run the beta version of iOS? If so, remove the profile and uninstall the beta and see if the iOS 16 update available.

How to uninstall iOS or iPadOS beta software - Apple Support

If you have downloaded iOS 15.7 and not installed you will need to delete that file. Go to Settings - General - iPhone Storage - check here for the file, then swipe left to delete. Restart the phone and check again for the update.