Hey Joan,
As long as the classes are created in ClassDex, they should be marked as “FULL” and unavailable for adding to the cart on the user page that is generated by the ClassDex shortcodes. If you added some classes directly to Cart66, that would create a situation where ClassDex would not be in control of their availability. If it says that the class is FULL on the ClassDex backend, then it will be full for the user. You can set the max number of students on the class edit page.
Maybe you could send me some screenshots of what is going on?
One other thought: if your site is utilizing page caching, you might want to turn that off for the pages where ClassDex shortcodes are embedded. The cache may be showing an old version of the page where the class is still available.
Hope that helps!
John