Help please

2009 Journey with 170k miles and a life time warranty. Overheating , car running fine then after 5 min temp spiked up then down. boiled over. First mechanic thought thermostat stuck and this was replaced. While test driving car again rapidly overheated and y to heater core broke cost 1 k to fix. First mechanic suggested tow car to dealer because he thought head gasket ruptured pressurized system and the ruptured the plastic y in the cooling system.

Now after repairing y dealer says no flow thru heater core. Heat was good prior to this."Chicago weather". Now dealer wants to replace core at 1800 bucks.
I still don't think they have found the problem.

Questions: will a plugged heater core cause a car to overheat. in 5 min or at all. Heater core flushed 30k miles ago.

water pump replaced 30k ago Also told bad water pump will cause this

Thanks for any help

 

I'm in the same boat! Keeps spitting coolant from the overflow tank. No overheat, just losing coolant from the tank and eventually when coolant runs out it will overheat.