Is this the actual outlook program on your computer or the webmail you are talking about? They changed the name of windows live (formerly hotmail) to Outlook now, just to add to the confusion.
If you did this on the local program on your computer, depending on your settings, you may be able to go to http://mail.mymts.net
and find those emails there. Microsoft uses POP3 or HTTP for email clients as far as I'm aware, so it's not real time communication between your computer and the Microsoft servers. Good luck. I recommend archiving emails instead of deleting. Email providers have plenty of space so don't worry
Authorized Service Provider (Contractor) for MTS Allstream. Any views expressed are my own.