My professor really emphasizes protecting against privacy leaks by always using accessors and mutators to access private instance variables; however, do I have to use the ge
No you can use directly your instance variables inside the class, you're not violating any "rule". Getters and setters are mandatory for others classes to access instance variables of a class to not violate the encapsulation principle (which is quite important in OO programming).
In the end it's a matter of choice, but you're saving one method call using your first example.