Cannot buy Cartel Coins as account isn't linked to EA?

The linked EA account has been disabled and data wiped, you will need to call swtor support when the lines are open  to have the account restored, you will need an email address not used on another ea /origin account previously

That EA account was created when the swtor account was created per this article

edit: there is a slim possibility that you could restore the EA account using the email address used to create the swtor account following the below directions, but usually with this it fails so you need to call.

If you’re restoring a deleted account and haven’t created a new EA Account with the same email address as your deleted account, you may be able to restore your deleted account through a password reset. If you’ve created a new EA Account with the same email, you’ll need to change the email address on the new account first in order to reset the password for the deleted one.

So I've gotta make a whole different email just for this? 

That is something you will have to discuss with swtor support when they look at the account