It doesn't sound like a water pump issue. If it's not in the red
while you are driving and in the red when you sit that is
due to the fact that your fans are not working and cooling the engine.
When in motion , you have outside air, but at a light, heat
builds up inside the bay with no way to cool off.

The other issue is that you should check your coolant for oil.
You may have blown a head gasket due to so much over heating and possibly warping your head.