When I click on "checking for updates" the wheel just spins. And spins and spins. Nothing happens.

Follow the steps at > Update macOS on Mac - Apple Support

If that doesn’t help, see > If an error occurred while updating or installing macOS - Apple Support

Also worth mentioning, third- party AV-ware, Cleaning-ware, Optimizing-ware and VPN’s can block your system from updating and from preforming correctly.

If all else fails try installing from the Safe Mode according to How to use safe mode on your Mac.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

What year model is your iMac?

see > Identify your iMac model - Apple Support

You need a 2015 or later iMac model to upgrade beyond Big Sur.