Someone on another post suggested that this may be Erythromelalgia. Look up the symptoms and see if they fit.
I have this just on my feet at night, but it's like the worst itch possible. I found that scratching makes it worse. I know it's really hard not to scratch, but don't. Don't even touch where it itches. It will go away faster if you leave it alone. Besides, the wounds you are making can get infected. If you read about it, it says the main complications are infections from scratching and frost bite (more on that later).
My doctor told me to stretch out my Achilles tendons because this helps stop the nerves from spasming or something (he'd never heard of the condition). The stretching does help. I also put on a ton of oatmeal-based lotion (I can't say what kind, because I'd be advertising, but you can find it) and put light socks on over it to keep it on.
Make sure everything you use is hypoallergenic. "Fragrance free" isn't good enough.
Also, keep the area that itches cool. I don't itch if my feet are cold (they have to be outside of the covers at all times). But don't dunk it in ice water or anything like that. People with this condition have gotten frost bite trying to stop the itch this way. Plus, I've found that if you try to get the area too cold, blood just rushes to the area and makes it hotter anyway.
I hope this gives some people some answers. Unfortunately, I haven't found any cures for this. If anyone finds anything, please PM me or repost here.