1997 Geo Metro Water Pump Bad? But not leaking

Hi my name is Connie Bustamante, and I have a problem.
I drive a 1997 Geo Metro 4Cyl. Automatic. I have owned this vehicle for about 8 yrs. My problem is that my temperature gauge gets really high and actually overheated last week. I have had this problem for about 2 months now. I do not have a leak but could not figure out why the temp. Gauge would get high. I checked to see if the fan worked. It works, thinking it might be the radiator I checked for a leak. No leak it holds the coolant fluid. Thinking it was the thermostat I changed it and still no luck. So then I figured it must be the temperature sensor. And still no luck in fixing the problem. So then I changed the hose on the bottom hose that connects to the radiator. Still gets hot, I took it to a shop thinking maybe it needs a coolant flush. However they decided to do a diagnostic check instead and $100 later they told me what I already knew. The fan, radiator, thermostat, temp. Sensor, radiator cap and hose is fine. They said everything was circulating okay. But it may be the water pump. I had the water pump, radiator and timing belt replaced 4 yrs. Ago. My water pump has no leak and seems to be in good condition. Could it be the water pump if it is not leaking and still looks good? I can not for the life of me figure out what is wrong with my car. Do you have any suggestions as to what could be wrong.