Hi Jh1,
Before moving on, I'd like to confirm the following information:
1. Have you verified your domain and changed the mailbox's suffix to your domain?
2. Which plan of Office 365 are you using?
Then, to troubleshoot this issue, you can perform the following steps:
1. Make sure the DNS records are configured correctly.
For Office 365 P1 plan, you can change the NS records to point to Office 365.
For Office 365 E plan, you can add the required DNS records at you DNS hosting provider.
2. Use a Hotmail mailbox to send a test email to the affected mailbox. If there is any DNR, please post it in the forum for further research.
For your reference:
Verify your domain and change name servers
Create DNS records for Office 365
Thanks,
Cherry Wang