Typically Outlook outboxes are attached to your local mailbox file (Offline Outlook Data File (.ost)). If you have wipe your computer than that means that you have wiped your local outbox.
The last place I would check is Outlook Online for your Outbox at https://outlook.live.com/mail -- If it is not there, then I am afraid your messages are gone.
Introduction to Outlook Data Files (.pst and .ost)
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