On traditional IBM mainframe what PSW is a special register that holds the address of the nest instruction to be executed?

Yes, the "Current PSW" contains machine state and next instruction address. It is a 64 bit register, and bits 33-63 (AMODE=31) or bits 40-63 (AMODE=24) contain the address of the next instruction to be executed. Certain "restartable" instructions, while in flight, will maintain the current instruction address until the sequence is complete, and certain exceptions, "early exceptions", will contain the current instruction address but, in general, the PSW (33-63) contains the address of the next instruction to execute.