An error occurred installing IOS 9.3.3 but there is no error code - What do I do?

Go to Settings > General > Storage & iCloud Usage > Manage Storage (the first one) > and if there is an update listed, delete it. Then restart the phone, go to Settings > General > Software Update and try downloading the update again.

If this does not help try updating through iTunes on your computer.

If you are doing this on the device itself, go to Settings>General>Storage & iCloud Usage>Storage>Manage Storage. Let the list of apps, photos, videos, etc load. Swipe down to the iOS software (if it is in the list), tap n it and delete it in the next screen.

Force restart your phone, No data is lost with this procedure. Hold down on the sleep and home buttons at the same time for about 10 seconds until the Apple logo appears on the screen.

Then go back to Settings>General>Software Update, download the software and try again.

If you are getting reminders there should be an update there. Did you look in that location after all content populated? It would appear as an IOS Update. The alternative is to update through iTunes in your computer.