Using Classic Outlook on Windows for personal email, calendar, and contact management
Hi. I'm Brian and I'll try to help.
Keep in mind that these are user-to-user forums. No one here can contact you directly
Since this forum is dedicated to using classic Outlook for Windows, I'll assume that's what you're using. Have you tried signing into the mailbox using a web browser at https://outlook.live.com/? Try it and see if the messages appear.
Are you using an Exchange account within classic Outlook to access your @outlook.com address? If you send a message to your @outlook.com address from your Gmail mailbox, does the message make it through? If not, does your Gmail address receive a non-delivery report? If it does, what is the reason for non-delivery contained in the report?