As foot itch is often a sign of internal problem, it is very often a symptom of an allergic reaction to something you eat, drink, put in your mouth (toothpaste, mouthwash, braces, dentures, lipstick, lip balm, etc) or something your skin get in touch with like detergents, laundry detergent, shoes, chemicals used for washing floors etc.
If you know your blood type, check the Blood Type Diet lists to see if you eat some avoids.
We are more likely to be allergic to foods and drinks from the avoid list.