While driving engine started revving high without shifting

Car has suddenly begun to act strange as I begin driving and increasing my speed it just starts revving, but won't automatically shift and continue to build speed. The only way I can get it to continue to go is to put it into 2. This is an automatic transmission car. We took it to a shop where the mechanic found a very worn cable that he felt might be part of the problem. He replaced it. Then he replaced transmission fluid. Car is still not shifting. Then it appeared to be overheating and before I could pull over, it shut off. It has started fine since then, but still has the high rpm's with reduced power. I am really hoping that it's not the transmission because I do not have that kind of money right now for a pricey repair. Do you have any suggestions on other things it might be? About a year ago it made a funny sound a few different times and mechanic thought it might be fuel pump, but hasn't done it since.