I'm sorry that you ran into trouble with this. You've signed in to Typekit with a different email address than the one you use for Creative Cloud. You will need to sign out of this account and sign in with the Adobe ID that you used for your Creative Cloud subscription in order to use the full font library.
I've sent details on the two accounts in reply to the email you sent to Typekit Support (firstname.lastname@example.org).
Once you are signed in to Typekit and the Creative Cloud desktop application with the Adobe ID that you use for your Creative Cloud subscription, you will be able select any of the fonts licensed for sync in the font library.
Please let me know if you have any other questions!