I've had itchy feet for two years, mostly at night. There is no rash and I don't itch anywhere else, so I'm not sure if we have the same thing. The doctors don't seem to take it very seriously, since all my tests come out fine and it doesn't respond to steroid creams or anything like that.
The only thing that seems to help is stretching out my Achilles tendons really well before I go to bed, then put on a lot of Aveeno lotion (soothing and hypo-allergenic), then put socks on over it. One note--this lotion seems to bleach certain fabrics, but I'd rather have patchy sheets than itchy feet.
Also, it's really important not to scratch, because it makes the itch worse. It is possible you are allergic to something, if not a medication then something in your environment. You may have developed an allergy to a soap or lotion you have used for years. You might also want to ask your doctor about antihistamines. I've also heard that stress can make it worse (but who wouldn't be stressed when they can't stop itching?)
I hope this helps.