It could be the torque converter, torque converter solenoid, or a failed or bent input shaft. If it comes to an abrupt halt with the wheels locked up, the differential could have a problem like a bad bearing.
In any case the best thing to do next is check the car for trouble codes. Since it is probably either the transmission or the differential, I would take it to a tranmsission specialist and not a standard repair shop. This is because automatic trnamissions take special expertise and the tranny and diff take specialized tools to work on them. A tranmission shop is most likely to diagnose the issue for the least amount of money.