Why would the back tire lock up?

You could have a seized rear brake caliper. Also, I'm assuming you took the emergency brake off, but if the car is equipped with auxiliary parking brake shoes (instead of using the disc brakes) they may not have disengaged. Brakes should not be taken lightly, especially with the brutal stop and go traffic in NYC. Take it for a checkup, even if it has to be towed. It is better than being in an accident and buying a new car. Here are links for estimates and trusted shops in your area: https://repairpal.com/estimator/buick/lesabre https://repairpal.com/buick-within-10-miles-of-brooklyn-new-york-11207