I'm dbowner on certain database (my account is on public role on server login but dbowner role on certain databases). Now when I try to add logins from server logins, I can only see sa account and my account. How can I add user to my databases from server logins?
You need administrator rights to be able to add users to your database. You should be able to add users if you have the "sysadmin" server role checked on your account properties.
There's a fuller description of the various roles here. This is relevant:
So if you can't add the "sysadmin" role, can you add the "securityadmin" role to the account?