Is my water pump shot?

I have a 2004 vw jetta wagon 2.0. A couple of weeks ago my vehicle overheated so I did what any resourceful male would do. I ordered a thermostat but it still boils on both sides of thermostat. I am wondering if it is the water pump that is shot and is not moving the water for me. I don’t know if my troubleshooting is done or if I am near a solution.

still under warantee? milage?

Lot’s of reasons for an engine to overheat…lost coolant, Not circulating the coolant…ie water pump bad, or blown head gasket…hot exhaust gas getting into cooling side of engine and superheating coolant to boiling point. Autozone has a lowner tool for checking radiator pressure. If you have a blown head gasket the tester will show a high pressure in the system and it usually jumps up high real fast. ( there is usually a user guide with the test kit.

no warr. 88000 runs normal for 10min in idle. than spikes to 260 then I shut off the engine. New thermostat. Temp warning light would go off periodically. There was a slight smell of coolant before failure. Than one day I tried to drive to work the car would overheat. if going down hill temp would drop.

Coolant level fine. faint smell of coolant present 8months before blown head gasket(I did not push the engine to overheat and warp) Air temp when failure happened -10F. There is no smoke in exhaust.