First off, I want to say Thanks in advance for any/all advice.

Here's what's going on.
Went on a long trip, 8+ hours (one direction) and the car ran GREAT, until we got to the mountains. Then it started overheating, like getting into the red, warnings ran across the info bar on the dash, alarm rang kind of overheating. No smoke was coming from the hood, but the check engine oil/change oil light came on along with check coolant. Ran fine on the flat, and small hills but over heated 3 or 4 times on the mountains. The last time it overheated at the summit there was white smoke coming out of the engine compartment. Drove in 3rd gear with the heater on high and it cooled the engine off and ran okay.
This is everything that has been done to it as far as I know as we haven't owned it long:

Water pump was replaced at a Cadillac/Chevy dealership garage.
Engine oil and filter were replaced.
Coolant drained and changed.
Thermostat was replaced. (was tested before put in)
Radiator was flushed, leak and flow tested and passed.
Radiator pressure cap was replaced.
Transmission fluid topped off.
Block tested

After all of the above was done, we tested it by heading up the mountain pass where it overheated (into the red w/warning lights on dash) and dumped the whole tank of radiator fluid out of the overflow tube on the side of the road. Limped it back where it overheated every few miles.

There's a hose that runs across the top of the radiator that has become very swollen and lifts the cover that fits over the top of it and the headlights. Does this mean that there's a blockage somewhere??

I'm at a loss at what is going on with the car as it is not leaking fluid and this just started happening.

Thank you again for any help...