I am with @m_hutley on this one. You are required to have an authorized email that’s setup with your mailing server on GoDaddy. If you don’t own an email that you have setup on GoDaddy, I don’t believe this will work. My initial post from last year was quite on point I believe. Most popular hosters now are taking action. Important Update: Managing email addresses for PHP/ASP mail scripts! - whois.com's friendly reminder
If you already own an email that you have created from GoDaddy’s control panel and it is a working email. Then you will have to figure out why it’s not sending emails through. I have had this issue before with my hoster, but that was only because they were switching mail servers. So they had changed the main outgoing server and have ported my actual domain with the subdomain mail.___.__ so that I only need to use that as outgoing server instead of theirs.
I honestly think you should be testing on a localhost first before you start doing it on live servers. You should never have to do it via live.