How do I unlock my apple account without recovery key

You only need it if you set one up. If you did then you really need it. Look for the piece of paper where you wrote it down.

Click on this link to discover 'How to generate a recovery key' --> How to generate a recovery key - Apple Support

With two-factor authentication and an Apple device, you have the option to generate a recovery key to help improve account security.

- "Creating a recovery key turns off account recovery. Using a recovery key is more secure, but it means that you’re responsible for maintaining access to your trusted devices and your recovery key. If you lose both of these items, you could be locked out of your account permanently."

A recovery key isn't required with two-factor authentication, but using one gives you more control over the security of your Apple ID. When you generate a new recovery key, you turn off other account recovery methods. Then the only way to reset your password or regain access to your account is to use your recovery key.