Where did my catalogs go following the latest update? I need help ASAP

You don't tell us what update you are referring to. You don't even tell us what software you are using.

So, I will guess that you are talking about Lightroom Classic. Please locate on any of your computer's internal or external hard disk any files whose name ends with .LRCAT (probably lower case). To do this, you have Windows Explorer search all disks for *.lrcat. Then to open these catalog files, find the biggest one (that's probably your main catalog) and double-click on it. If that's not the right catalog file, try double-clicking on each catalog found until you find the right catalog file.

Unfortunately you don't have gave us any informations about your system and details about your issue. So all proposed solutions are a look into a crystal ball.

... Following the update, I can no longer access any of my catalogs. ...

By @bernicey75134016

From which version to which version do you have updated?

What do you mean with "... no longer access any of my catalogs"? What do you try and get you any error messages?

Please check if there's a .lock file next to the LR catalog in the appropriate folder.

If  there's such a .lock file it must be deleted manually.

More informations about this, you'll find here: 

The Lightroom catalog cannot be opened because another application already has it opened - lrcat.lock (adobe.com)

...I tried going to the backups, checking the folders labeled with the correct catalog to no avail. I am a relatively new user and always backup my catalogs, but not to the cloud.  I guess I assumed that by hitting the backup button a copy of the catalog was backed up.   ...

By @bernicey75134016

If you're doing a backup on ending Lightroom a .zip file including the catalog is created on the appropriate folder. Before you can access the catalog you have to unzip this backup file.

Disaster strikes - a corrupted catalog! | The Lightroom Queen