in your case, you are a beginner in the subject if you do it for CM Installer, which is compatible with the S3 Sprint, besides the Intl S3, S4, S2, Nexus different there ...
Then you can update the version of CM but you have to do so.
Settings -> Phone Information -> Cyanogenmod Updates.
On the second screen where it says "type of updates" and put all updates the screen when finished settings.
Now download an update, click on it, accept the conditions and automatically install.