Hi Jay,
You've conflated 2 things. Wanting a head gasket and your engine having cooling system issues.
As you know, most everyone who works on cars are trouble shooters. We like to fix stuff. Like FF alluded to, there are other things that can cause cooling system issues and all have accompanied symptoms.
So yes, some symptoms may point to having to replace your head gasket and I'm sure someone on here has the head gasket info (not me).
What is the water temp? A stuck thermostat?
Regards,
RJ