Can you get addicted to the drug phentermine?

Sure. Phentermine is a stimulant & fully capable of being the source of addiction. There is a difference between physiological tolerance &/or withdrawal -vs- addiction. To be addicted you need one of the biological features (tolerance or withdrawal), loss of control (despite negative consequences), & salience (it becomes an important part of your life).
Yes. Any medication once you use constantly the body develops a new homeostasis and when you stop the medication the body goes through disturbance to re-establish its original state. Depending on the severity of withdrawal the amount of physical dependence will be evident. All medications better to slowly taper and withdraw - this includes the nutrients too.