If you are seeing strange usage spikes in your SMTP relays, it's possible your server was compromised. A bad actor might have gained access through a password or uploaded a malicious script to send emails. Another possiblity is that a vulnerability was exploited on your website to send emails. If you have a contact form on your site or some other page that sends emails, it's also possible that is being abused.
I suggest that you do a thorough review of your site and scripting to look for any issues. You might also want to resent any passwords associated with your GoDaddy account and server. If you are using WordPress or a similar CMS, you may want to reset the admin passwords and/or remove unneeded user/author accounts.