Hi AnAverageJo,
Sorry for the inconvenience caused by the issue.
Based on the current situation, I would like to collect more information for troubleshooting:
1. As I understand it, you have added the Hotmail account in Outlook (do you have added the Office 365 account in Outlook?), and send the same email to Office 365 several times, but this account has only received one email. Is this correct?
2. Which Office 365 plan you are using, Office 365 pre-upgrade or Office 365 after-upgrade.
3. Can you send emails and receive emails from others as well in OWA (http://mail.office365.com/)?
I also noticed that you have some concerns about adding an Hotmail account in Outlook and keeps getting the error. I recommend you contact the Hotmail support to get a better support for the issue. They are professional in this kind of the issue. Thanks for your understanding.
Here is the link: http://windows.microsoft.com/en-us/hotmail/hotmail-help
Best Regards,
Anna Shi