Remove the beta profile. I did the same thing. Once it's removed 16.1 will show.
But 16.2 is not yet in public beta, so no need to rush, unless you have the developer license.
The problem was when I first checked for an update, before I installed the profile, the update wasn't showing (16.1), so I installed the profile, and this was a mistake. I guess it just takes a little while for 16.1 to show up after you set-up the iPad. I think several people are doing this.