I am locked out so I can't install Updates

You will have set a pasword when you installed ZorinOS. I don't know why you have been looking in your BIOS for ZorinOS passwords.
What error message do you see when attempting to input your password?

See this for some explaination re Authentication Password.

and

The solution suggested there was re-install ZorinOS again. You should backup your /home partition containing your data before doing that.

EDIT:
I did a webserach using Ubuntu 20.04 which ZorinOS is based. I found this item, but seems quite involved compared to a reinstallation and I do not intend to test that method myself.