this sounds like the thermostat is stuck shut so I'd 1st move on by replacing that
Whilst the thermostat is being replaced you might as well also reverse flush the cooling circuit (remove top hose to rad and use a hosepipe to push water into the engine until you get clear water out of the radiator hose) and top up with 30-50% fresh antifreeze. Also check that the small diameter bleed hoses that run from the top of the radiator and the top of the engine aren't blocked as this allow the air to vent back to the header tank automatically.
If you still have a problem then check that the water pump impeller / turbine isn't spinning on its shaft. You should be able to achieve this by removing the bottom hose from the engine and use a screwdriver or similar to feel for the water pump impeller blades, whilst your assistant turns the engine over by hand.
If you can stop the impeller with slight pressure from the screwdriver the pump needs replacing.
Also its possible the belt is slipping so its worth replacing its especially if the rubber ribs are cracked or it looks shiny on flat side of the belt - while its off check that the tensioner and other pulleys all spin freely the exception to this is the AC pump ( if fitted)
I'd also suggest ensuring that you've got all the air out of the system as this sort of episode can leave pockets of air trapped and prevent the coolant from circulating properly.
So check that the small hoses that run from the top of the engine and radiator that run back to the header / expansion tank are free flowing and not blocked
If these are OK then remove the tank pressure cap and run the engine from cold with the heater set to full hot
As the engine starts to warm, squeeze the large hoses running to the radiator to help displace any air - all the time keeping an eye on the level in the header tank, making sure it doesn't drop below the minimum and open any bleed screws built into the top cooling hoses - closing them off as soon as they start to gush water
Once the engine is up to temperature the tank should be quite full. Switch the engine off and leave it to cool
Then top up to the mark once its all cold and replace the cap