jc9922: It sounds like you and your wife got a pretty good case of AMS (Acute Mountain Sickness). I don't know why they stuck "Acute" in front of it -- it is just plain Mountain Sickness. Many people start feeling the effects on the switchbacks, which is where your issues seem to have begun.
Most people need to spend two nights above 8000' elevation to help acclimate. Staying at 10,000' is even better.
Eating small amounts and often, especially lower on the trail (before AMS kills the appetite) is the best way to hike Whitney.