You've followed the instructions to set up Office 365 from ITEGY-Distinctive Technology Services on an external domain, and now you're getting the message Check your MX records and try again, or not receiving email after 48 hours. You may need to delete some old DNS records that are no longer needed.
It can take up to 24 hours for these changes to go into effect. Sign back in to the ITEGY-Distinctive Technology Services account where you're setting up Office 365 and see if your new email accounts are working. If not, please call Support.