Why can't you ask the apartment manager if you can borrow a plunger? You have a problem, deal with it. There is no shame it happens to everyone at some point. If you worry about what they think and they ask say a friend plugged it.
I also agree with the other post saying to just buy one at the dollar store. You don't "order" things you need right now.
I'm thinking its all a show/lie. When it doesn't show up he is to be able to tell the American people that Ukraine is driving up prices and attacking american fuel...