First there is no Lightroom CC. There is Lightroom (NO CC after the name), the Cloud centric version, and Lightroom Classic the traditional desktop version.
Although I am not that familiar with the Lightroom plan AFAIK it does not really include LR Classic. The standard Photography plan that inlcudes LR and Photoshop and only 20GBs of Adobe cloud storage does "Allow" (Allow is the Key word here) you to install Lightroom, cloud centric version, but you still only get the 20GBs of storage space.
The plan you bought includes 100GBs of cloud storage and no access to LR Classic or Photoshop.
If you want to change plans look at this Adobe webpage.