I had that problem also for a few years. I never consulted a doctor about it or anything, but I was tested for allergies and it turns out I'm allergic to soy, dustmites, cats, and other various things.
They never told me anything about itchy palms and feet being symptoms of allergies, though I've come to realize that my itchiness only comes back when I quit taking my allergy medicine, and it goes away when I take it again.
I wouldn't say--if you have allergies at all--that they are the same as mine, but my dustmite allergy seems to be the most logical reason for the itchiness (as it's a bit hard to find soy products randomly scattered about on the ground, especially in and around the house).
I'd go check with your doctor, especially if you seem to have other allergy symptoms (sneezing, runny nose, excessive throat clearing, etc.). This is the only logical explanation I could come up with. Hope that helps.
Palms Itch Terribly! 
