Just tossing this out there... do you have any type of fungus? Athlete's foot or something? I remember, like 10 years ago, the first day I had athlete's foot (or realized it). Business as usual and then SUDDENLY my feet ITCHED like CRAZY and I could not possibly scratch them enough. Topical over-the-counter ointments and powders, etc. solved that problem but only when I used them, which was years. I used them everyday to keep the problem at bay. Moving to the equator helped, as now I wear sandals everyday to keep them ventilated, as well as using a foot file to exfoliate everyday. I'm sure there's body imbalances and terrible stuff involved, but the thing that helped the MOST was urine therapy. Kept the morning's first urine all day, and that evening (a bit "old" by then) I made some feet bags and slept all night with that on my feet. Sorta stung a wee bit and I was nervous all night that it would leak onto the bed. BUT the next morning they were so smooth and since then, no problems, although I still keep them exfoliated. I know it's gross but anyway I highly recommend that to anyone with athlete's foot.
But your symptoms don't sound exactly like mine - I am just tossing it out there as a possibility.