The CCC includes the drivers for the graphics card. There is a note on the CCC download page that indicates the following message:
Before installing this driver, please ensure you have uninstalled the previous driver using the Add/Remove programs option in the Control Panel and also deleted the installation folder for the previous driver. This folder can be found at the following locations:
C:/AMD/support/14-4-win7-win8-win8.1-64-dd-ccc-whql
or
C:/AMD/support/14-4-win7-win8-win8.1-32-dd-ccc-whql
I would probably run display driver uninstaller found here:
http://www.guru3d.com/files-get/display-driver-uninstal...
and then delete the old folder as outlined in the note above, then reinstall the CCC 14.4 package.