Are you asking about Business Catalyst or Creative Cloud?
BC does not come with Creative cloud no. But if you refering to Creative Cloud itself you need to download the app for that, login and then run that and choose the apps you want to install.
Did you install Application manager, if not, use this link to install it,
You should be able to install all the program, without paying extra. Just make sure that you are logged in with the same account on which you have purchased the subscription. In case of any issue, I would suggest to reach out to Creative cloud support team using this link
Do let me know if you have any question.
Got it! Thank you.