Water pump/timing belt replacement

My car was starting to overheat and leak antifreeze, before I had a chance to get it in the timing belt snapped and the car broke down. I replaced the timing belt, but I am still having the overheating/leaking issue. From what I have heard when the timing belt is replaced in these cars the water pump should also be replaced. It has a rebuilt engine in it with only 27,000 miles on it so far, and had a new transmission put in at 160,000 miles, both were done prior to me buying the car just two years ago. Besides the overheating problem I have had no other issues with the car since the timing belt was replaced. I am wondering if I just need to replace the water pump and the timing belt will still be okay? I have hardly driven it since having the timing belt replaced in fear of messing it up even more. Any advice on this would be very helpful!