What version of OSX do you have?
What version number of After Effects do you have (down to the last decimal)?
After Effects 12.0 and OS X 10.9.3
Your AE is not up to date. 12.0 will not work on OSX 10.9.3
Mavericks broke some things.
You need the latest update to CC which is 126.96.36.199 (although they're releasing another update later this month).
Although, technically you don't need the latest update as the 12.0.1 update made AE work with Mavericks
To get that version do I need to download it from the Adobe website instead of CC?
Creative Cloud should give you the update. Your CC app may be in need of an update itself.
But yes; you can get the update from Adobe's site as well. This After Effects CC (12.2.1) bug-fix update page has instructions and info.