But that's the strange thing, I obviously have purchased it.
As I said, it's most likely a registration issue then. If you used a different email address on the store (and occasionally even if you did), the TA serial won't be automatically registered. And you do need to have DL and DA already registered on the same account, if you don't already.
If you used a different email on the store, you'll need to request an email merge from support to get TA registered to the same account. If not, then you should be able to just register the serial manually in SDC.