My Mac crashes and shuts down when charger is unplugged, not immediately
Unfortunately, you have to make that journey as there’s really nothing you can do. 


if it’s the battery or hardware, which I suspect, it’s got to go in for service
if it’s an update or macOS issue, your IT department will have to address since it’s locked down as you describe
even some of the diagnostic procedures will require sudo access which you stated you don’t have means you have to take it in


When an IT department locks down an asset like yours, it’s best to let them handle things. They should have loaners and/or replacements at the ready.  Make sure when you communicate to them, emphasize that it stops your work (just some lingo to use to prioritize you in the  queue).