Sending, receiving, and organizing email in Outlook.com
Hi. I'm Brian and I'll try to help.
Typically, an institution's accounts are not personal accounts and do not use the same servers to hold the mailbox. Are you using an address that ends in the school's domain or one that ends with a Microsoft domain? When you tried to send a message to that address, did you receive a non-delivery report? That report should explain why the message failed delivery. If you did, include it here exactly as it appears on your screen, but mask any real addresses it contains so they don't become public.