Is there any way to download the messages app off of the app store (I've looked and haven't found it. Is it called something else there?) How could I get the messages app on my computer?
Edit: I have checked to make sure my spotlight works properly, and looked through my applications folder. It is not present.
Messages.app comes bundled with OS X, it seems that it got deleted somehow.
To get the Messages app again (or any other pre-installed OS X app that is not available on the App Store), you will have to re-install OS X. The process does not erase any data.
Alternatively, if you know someone who has the same OS X, you could copy
Messages.app from their machine and paste it in your Applications folder.