Can't login after updating software
There are really two problems here:


Can you make a new admin account in single user mode and use the Mac?
Do you need to recover from the failed EFI update or will it work once you address #1.


It's not possible to do anything other than guess which is the real cause. I will try to give steps for either in case you want to work this out and come back and ask a more specific question once you've narrowed down which is the failure here.

In the prior - you can either boot from an external OS and try to fix the account and/or boot situation. 

In the latter - booting from an external OS is ideal to attempt the EFI update again without further harming the normal user and OS. It also allows a backup if needed and you did not make one immediately prior to running the EFI updates.

It's rare for an EFI to get stuck when there isn't another hardware or drive corruption issue - but this is one of the reasons why many are in the habit of


always backing up before any update that requires a reboot
rebooting and running a clean backup with nothing running, then rebooting and running the EFI update as the first task of the OS.


Recovering from an EFI update failure often involves a trip to the repair center since EFI is the initial bootstrap mechanism of the hardware to run in the first place.