Water pump Or Thermostat?

The water temp. gauge in my car was fluctuation from normal op. temp to starting temp., Drove car about 10 miles parked and the over flow hose exploded!
(small hose from top left side of the water pump housing)

I also pulled the thermostat and put it in boiling water and it did not open after about 5min.

Chevy Lumina 93 3.1L euro sedan 4dr

thnx