I figured that because I have two radiator caps one rated at 15psi and and one at 16psi I should be able to use a pump with high enough pressure to refill the radiator whislt the system is still under pressure.
I will attach the pump to the 16 psi cap that will should prevent backflow to the pump as the excess pressure should leave through the 15psi cap. I want to prevent backflow because I am trying to keep the pump clean for later use with drinking water.
I'm just going to guess that you've got a leaking head gasket. The coolant has to be going somewhere, and if you can't see a leak it's probably entering one or more cylinders through the blown head gasket and going out the exhaust pipe. Depends on the car and your DIY skills, but it could be a cheap-ish fix. I'd also be leery of topping up the cooling system with plain water - that'll dilute your coolant and reduce its antifreeze and boilover protection.