May be the selected language in Adobe Application Manager to download the software is diffrent from the language in which software is already installed on your computer.
There is no need to download the software again you just need to activate the subscription.
If software is presently running in trial mode then launch the software, you will get an option to license the software then enter your Adobe ID and password on which you have purchased the subscription. It should work now.
If software is already activated with some serial numnber then Launch any software of creative cloud and deactive the Serial number from the Help menu by selecting Deactivate option. After deactivating launch the software and license the software with Adobe ID and password.