Hi,
The first thing I need you to do is reboot your iPhone.
To do this navigate to General - Shutdown and follow the prompts to do so.
Once your iPhone has shut down, reboot it and return back to the iPhone settings and check to see if your mobile data and if your software update has been installed.
If it hasn't, I would remove and reinsert your SIM card back into your phone.
Then double-check your wifi connection and make sure you have an ACTIVE wireless connection. If this works, you should be able to install the software update.
If not, plug your iPhone into iTunes on a Windows or macOS Device and update manually through the suggested prompts on iTunes.
This should bypass the manual way of updating through your iPhone settings.
If this doesn't work let me know, and we can explore some other alternatives.