2000 Other Saturn Models bad idling

I drive a 2000 saturn ls. The other day I started my car and the engine started revving and the rpm gauge shot up to 3 instantly. I put it in reverse and it stopped. But when I put it in drive the car idles really fast. It gets up to 35 mph without putting my foot on the gas. I went to autozone and they told me it was the idle air control valve. I have to hold the brakes down fairly tight to get it to stop. I just don't know how reliable autozone is.
also, I believe my water pump is broke because my car overheats a lot and I have to drive with water jugs. Could this have anything to do with it?