Some times you can get a Bad radiator it happens I had one with 1 pound of sand inside it then another was half plugged up YES these are NEW radiators I'm talking about.

Always flush out any new rad you get you may find its full of dirt/grit. This can trash your water pump so be warned.

You may have vapor lock sounds like it.

 

I was told today to try to bypass my heater core since my heat hasn't worked in a few years maybe there is a blockage. Could that actually cause an overheating problem?

 

Is your hose still compressing?

If so its vapor lock you have air in the system check your cap I know you have a new cap but it may be a cheap crap cap get a stant cap stant meaning the brand name.

So much cheap bad China crap out now

Is the cap a bit hard to screw on if not its a bad cap

No on the heater core will not make any difference just means no heat in your cab

 

I got my truck out of the shop my heads were warped. So $800 later I have machined heads new gaskets and new plugs/wires.

 

probably because of the 7 pound cap. boiling point is 212 at sea level and at 7PSI I'd guess it to be around 230, 50/50 mix add 15 degrees. I have a 20 pound cap and 50/50 mix boiling point is around 275 (water is 260).