need some help- rough idle problem

[cheatham]

this is a new problem and mostly only during cold starts. after warming up and going to idle my truck is running very rough. also it sounds like the water pump is shot (that rattling sound). I would think this could also be the reason it is idling rough and finally dying. I dont have the problem after driving for 10 minutes. but when i took the belt off and turned the pump by hand it is smooth and quiet. could it be shot anyway and is it likely the problem (ignition and fuel have not been a problem and are set correctly)

thanks in advance
Jack