My professor suggested that maybe i could add physical stops on this screw, and then measure the current to the motor. When the plunger hits a stop, the motor current will spike telling the arduino to "stop" the motor.
Ask your prof if he as actually tried doing this?
I did this in my final year project back in 1974.
In principal it is easy. A series resistor in the ground of the motor and measure the voltage across the resistor. As the current increases so does the voltage.
BUT when the motor first turns on there is a current surge that is almost equal to the surge you get when it stalls. It is bad for the motor to keep stalling it like this and is a very poor design for something that is meant to run reliably over the long term. A contact less sensor like a hall effect is the best solution. The added cost is negligible especially on a mass produced product.