My mac show me as standard user only and doesn't accept my username or password

Is this what you did?

See if you can create a new administrator account by restarting the Setup Assistant:

1. Boot into Single User Mode: Start/restart your Mac. As soon as you hear the startup tone, press and hold ⌘ + S until you see a black screen with white lettering. (If you end up back on the login screen after a flash of the black screen with white lettering, enter your password and it will return to the black screen.)
2. Check and repair the drive by typing /sbin/fsck -fy then ↩ enter - as directed by the on-screen text.
3. Mount the drive as read-write by typing /sbin/mount -uw / then ↩ enter.
4. Remove the Apple Setup Done file by typing rm /var/db/.AppleSetupDone then ↩ enter.
5. Reboot by typing reboot then ↩ enter.
6. Complete the setup process, creating a new admin account.

Be very careful to notice the spaces in those Terminal Commands.

Once you've done that the computer reboots and it's like the first time you used the machine, except all your data will still be there. Your old accounts are all safe. From there you just change all other account passwords in the account preferences!!

You're welcome. So when you ran the command to remove .applesetupdone then restarted it didn't ask to create a new admin account as described? I've seen that method described from more than one source. I don't know why it didn't work.

See this article: https://www.lifewire.com/create-new-admin-account-for-login-issues-2259976

I just looked at the article. To start up in single user mode, you need to hold command + S, not command + R.

Good work, thanks. :)