What's changed is Cox no longer allows "relaying". Prior to the recent change, if you used a mail server other than a cox server, for example myserver.net, with Outlook or other email program, you had to have the account settings for receiving email to something like mail.myserver.net or pop.myserver.net to read those emails, but you could use smtp.west.cox.net (or the east coast version) for the "outgoing" (sending) server, which is "relaying". Cox mail server was sending the email as if it was sent from "myserver.net".
With the recent change, if your'e using a mail server other than a cox server, you have to go into the account settings and change the outgoing server to something like "smtp.myserver.net", along with other settings such as outgoing server requires login - using same name and password as incoming server, and also set the port addresses as needed for sending email via "smtp.myserver.net" (you'll have to get the port addresses as specified by "myserver.net").
It would have helped if the error message was "relaying no longer allowed", instead of "relaying not allowed", since a typical user would have no clue this was due to a change at Cox for something that was previously allowed, but is no longer allowed. With the current error message "relaying not allowed", a typical user would have no clue the error was due to a change in the way Cox handles outgoing emails for non-Cox email servers, misleading the user into thinking the problem is due to some other unknown issue.