Does your Cloud subscription show on your account page?
https://www.adobe.com/account.html for subscriptions on your Adobe page
Cloud programs do not use serial numbers... you log in to your paid Cloud account to download & install & activate... you MAY need to log out of the Cloud and restart your computer and log back in to the Cloud for things to work
Some general information for a Cloud subscription
Log out of your Cloud account... Restart your computer... Log in to your paid Cloud account