I don't have a file vault recovery key - and i am locked out of my computer

Gulp!

If you choose iCloud, the recovery key isn’t stored loosely in iCloud Drive or as a file, but it’s tied into behind-the-scenes account information that Apple maintains. It’s fully encrypted in such a way that even Apple doesn’t have access to the unencrypted recovery key data, but Apple can deliver the encrypted recovery key to your Mac if you need to reset your password. You never see the recovery key nor have to enter it in this configuration. (The process is a little involved: Apple describes it in the section “Reset using the Reset Password assistant (FileVault must be on)” in this support document.)

If you choose the other path, where FileVault generates a recovery key and displays it, you need to make sure and write it down or enter it electronically, and store it securely in such a way that you’ll have access even when your Mac can’t be booted. I use 1Password’s secure notes for this purpose, but any method of storage that’s reliable, secure, and accessible will work.

How to find your FileVault recovery key in macOS | Macworld

Do you have Filevault enabled? If not and you have a 2017 or earlier Mac, then your data can be accessed by either booting from an external boot drive or by putting the Mac into Target Disk Mode to connect it to another Mac. If Filevault is enabled or you have a 2018+ Mac with a T2 security chip or M1/M2 Apple Silicon, then you will need the password or recovery key to access the data.