We just upgraded to a paid version and 14 days later our forms are disabled because of form views? Please explain.

If you form is embedded to a high traffic page, each time the page is loaded, the form will also be loaded.  Each time the form is loaded, that counts as a view.  Your account is indeed over limit for form views.  Replacing the embedded form with a link to the form will ensure only the users who would like to fill out the form are viewing it.

Here's an article that explains why it was implemented and what this limit does https://www.jotform.com/blog/191-Announcing-Pricing-Modification-Form-View-Limits.

If you want unlimited form views limit, you can allow JotForm to display ad (Powered By JotForm) in the footer section of your forms. To do so, just check "JotForm Footer" on your settings page https://www.jotform.com/myaccount/settings. You should see "unlimited used" in your account status after that under Form Views.