With any decent RC car, yes. You can change the transmitter and you need to change the receiver as well which comes with a transmitter. Just plug the connectors from the speed controler and steering servo over to the new receiver and recalibrate the speed controller. But....

Your car seems to have an all in one module which is very comon with such small and cheap cars. The receiver, speed controller and a part of the steering servo are in one housing that can not be pulled apart. Then you do need to change it all which will bring you close to a new car.

If it mechanically gets stuck at full throttle I would open the transmitter. Otherwise if you still have warranty I would go into that direction.