Apple has just released the new beta and most users were able to update their devices to the latest release over-the-air. However many users also complained about not getting the update, with iOS telling them their version is up to date. I got the same problem and was not able to install the new beta on my device, until I tried a number of solutions. The issue was resolved when I removed the Configuration profile from my iPhone and downloaded the new one again from the developer center.
So if you are having the same issue of iOS beta not getting installed on your device, then you can follow these simple steps to resolve this issue. Open Settings and go to General > Software Update. If you get the notice that iOS is up to date, then go back on ‘General‘ screen and scroll down until you find the ‘Profiles‘ option. From the Profiles page tap on the iOS Beta Software Profile and from the next screen remove it by tapping on the Delete Profile button.
Once the profile is removed download it again from the developer center. After it has been installed reboot your iPhone, open Settings and try again. If you still get the same message, then open App Switcher and close the Settings app. Then finally open it again and head to Software Updates. Now you should be able to install the update.