I'm having trouble learning about electronics?

It's impossible to diagnose a circuit without a circuit diagram, but a 3V increase in voltage should not be "burning" transistors. That suggests to me either you do not have a suitable current-liniting resistor on the transistor base or you are asking it to pass too much current between collector and emitter - is it possible that it is being shorted or your transistor is under-rated? Another possibilty than occurs to me is are you protecting your circuit from back-EMF generated in the motor? If you are unsure then a reverse-biased diode wired across the motor connection is a good idea - a 1N4001 will be suitable for smallish motors.