I know how important keeping your devices up to date is, and I want to help you get your iPhone updated.
Let's start by restarting your iPhone:
Restart your iPhone, iPad, or iPod touch - Apple Support
After restarting, try to run the install again. If it hangs up again, follow the steps at this article:
Get help with over-the-air iOS updates - Apple Support
Let me know if that solves it for you.
Thanks for using the Apple Support Communities.