62 GMC Heater Water Pump Cooling issues.

[Smo_King]

Ok held out long as I could... 62 GmC 305v6 LWB

Heater does not heat. Taken apart, flushed core, etc... on to, think my pump is out?

Replaced thermostat from 180>195
Flushed system took all hoses off replaced hoses and new fluids.
Burped her best I could water just over flowed out cap.
Coil is in the bottom hose.
Belts ok and pulleys all turn.
Fan works.
New oil and filter.
No noticable weepage.
Radiator appears to have been replaced. Guessing in 98ish. Its only been 15 miles since 98-99
Cap seems ok 13lbs going to get a 14-16 next week.

This all started after pulling hoses to chk heater core and connections. Will overheat idling in about 5mins (or get to H) Guage is OEM, Cleaned contacts and assume guage and temp sensor are somewhat correct. IR after running then shut off near therm area outside, reads 190ish.

-I pulled the heater hose from thermostat area which I assume is out and started engine and reved, and nothing came out.
-There was significant calcium but no chucnks of rust when I flushed system. -Water is really hard aound here. Thats all I got.
-Radiator appears to have been replaced. Guessing in 98ish. Its only been 15 miles since 98-99

Can I get lucky and pull pump and unclogg?
Does heater have a thermostat as well?
Is this short or long? And whats the cheapest way to replace for now, rebuild kit, another model anything in the 20-30 range? I dont have a press but pretty sure a neighbor would.