I don't know what thunderbird is but regardless a lot of people cannot send emails with Cox since Jan 24. I managed to get around the problem on my ipad by using my daughter's smtp server credentials on port 587. But that workaround didn't work on Windows 10 Mail.
Your username should be the [primary] username - like the one you would use to login to cox.net.
Your other settings look fine for the outgoing server.
In Thunderbird (52.6.0), click on your account name, then "View settings for this account". Right there on that pop-up look down near the bottom in the RIGHT-hand block - there is a 'Outgoing Server (SMTP)' setting that selects the outgoing server for that account. Make sure that points to the correct outgoing server you have defined in the 'Outgoing Server (SMTP)' Settings on the LEFT side where you set up the outgoing servers that can be used by all accounts. It should be the 'smtp.cox.net' one.