I understand you're having some trouble updating to iOS 11. No problem, let me see what I can do to help. For starters, let's it doesn't sound like using the built-in updater is going to work, but you're welcome to check out this article and give it another shot: Get help with over-the-air iOS updates - Apple Support
If that doesn't work, we'll need to use iTunes on a computer to initiate the update. Make sure the computer is running the most current software version available by checking here if you're using a Mac , and here if you're using a PC . You'll also want to make sure that you have the most current version of iTunes available: Update to the latest version of iTunes - Apple Support
This last item is more common among PC users, but if you're using a third-party security software, often times they'll have a built-in firewall that can create problems when iTunes tries to connect with our servers, so make sure you temporarily disable the firewall before starting the update in iTunes. With that out of the way, it's time to start the update:
Update the iOS on your iPhone, iPad, or iPod touch - Apple Support
Update your device using iTunes
If you can’t update wirelessly on your iOS device, you can update manually using iTunes on a computer that you trust. If your computer is using Personal Hotspot on the iOS device that you’re updating, connect your computer to a different Wi-Fi or Ethernet network before you update.
That should be all there is to it, but if you're run into problems updating this way, make note of any error messages you get. iTunes is designed to report specific information about the reason behind an error, so knowing the exact message usually indicates why it happened, too.
Just keep me posted so we can keep working together if need be. Cheers!