She probably didn't tell anybody she broke the tube, because, you know, they might yell at her and it may cost her a bit of money if they discover she was clumsy. So she just went home and when she felt bad, went to the hospital. Where nobody knew shit about the plague, as expected - when a person with respiratory symptoms in the autumn shows up in a hospital, nobody thinks "let's test her for plague". When she died, and when they learned where she worked, probably some major "oh shit!" lightbulbs gone up, but by then it was a done deed.