There was a forum post for a similar issue over a year ago. That was just after a Cox Webmail update and there were still a few issues. But, I don't think the OP posted their solution. The first thing I would do is to delete myemail.cox.net cookies and close your browser. Note: you don't need to delete all your cookies. When you access webmail the next time, your webmail cookies will be re-created. I can't guarantee that will fix it, but it won't hurt anything.
Yes, that is a legit page for not for the customer email sign-in. Please delete your cookies and cache on the browser that you are using and delete the saved, bookmarked, or favorite link you have saved. Please type myemail.cox.net in the browser bar and it will take you to the email sign-in page. If you have any other issues. Please reach us on Twitter at @CoxHelp, visit us on Facebook, or email us at firstname.lastname@example.org. Provide us the name on the account with the complete service address with a link to this thread so we can get started.