Problems when Sending email to distribution list I'm a part of

Issue:

When I send any mail to a distribution list I'm a member of (with Dlist in to: field, or cc'd, etc), my sent message arrives as a new unread email in my inbox. This new message arrives in both outlook 2010, and also in OWA

I'm using Outlook 2010

Office 365 Exchange account

Usually (before we migrated to office 365) when I send a message to a distribution list I'm a member of, my message goes to sent items, and doesn't pop up in my inbox as a new unread message like its doing now.

Any ideas?

Thanks!