Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hi. I'm Brian and I'll try to help.
All Hotmail.com addresses are also Outlook.com addresses. There is no reason to create a new address unless you want to change the domain. That said, it sounds like you created a completely new account. Since it is a separate account, naturally you won't be able to see the Hotmail.com account's email in your Outlook.com mailbox. The proper way to change from an address ending in @hotmail.com to one ending in @outlook.com is to visit https://account.live.com/names/manage using your @hotmail.com address and add a new alias there that ends in @outlook.com. Then both addresses will refer to the exact same account and have equal access to the same data, like email, calendar and contacts. You cannot add an existing @outlook.com address as an alias to another account.
Why not just continue using the @hotmail.com address? You should still be able to log into that account using that address and its attendant password unless you deleted the account.