1) You could derive separate BalanceInquiry classes. One for checking, one for savings. Probably overkill if the logic is the same for both.
2) As your professor suggested, you could add a bool argument to BalanceInquiry's constructor to indicate if the inquiry is for savings or checking.
BTW, you have a memory leak in your program. Your ATM is eventually going to run out of memory and crash.
Line 130: You create a BalanceInquiry object assigned to tempPtr.
Line 136,141,146 You create new objects assigned to tempPtr without deleting the old object.