Unless your catalog and all of your images are on an external hard drive, or unless you backed everything up, then I'm afraid there's not much that can be done. Sorry.
It all depends on what you mean by "I backed up my files". If the catalog (or the weekly catalog backups) are included in "your files" then you are saved (or partly so). If not, the catalog is gone.
When you "backed up" all your files, did you back up the Pictures folder?
The default location for the Lightroom Catalog on Mac is in the Pictures folder of the user. The new Lightroom CC puts the catalog into the "Lightroom" folder. inside are the files:
(name of your catalog)Catalog.lrcat
(name of your catalog)Catalog Previews.lrdata
and if you Smart Previews you would also have a third file named
(name of your catalog)Catalog Smart Previews.lrdata
Your images themselves would be anywhere you originally put them - in your documents folder, on an external drive , or where ever.
Also, even if you did not back up your main Lightroom catalog, if you had set the preference to have Lightroom back up the catalog when you quit Lightroom, and if you set the preference to put the back up in a different location (which you should), you might at least have the back up catalog.
The Back up catalog files could be found in the location you had set in a folder labeled by date and time, such as 2015-05-04 1728 (meaning May 4, 2015 at 5:28 pm). Inside that folder would be a zipped file with your catalog. In this case, you would only have to start up using the back up catalog, relink your image files, and then let Lightroom rebuild previews.