The SQL login you created isn't associated with the local Windows account. You've created a stand-alone login within SQL, which is why it asked you to create a new password instead of using the password of your Windows user. Here is a script that will create the login, and then add it to the 'sysadmin' server role.

USE [master]

GO

CREATE LOGIN [MyDBServer\LocalAccount] FROM WINDOWS WITH DEFAULT_DATABASE=[master]

GO

EXEC sp_addsrvrolemember 'MyDBServer\LocalAccount', 'sysadmin'

GO