What could cause severe itching on the sole of the foot and underarms? no visible rash

May be nerve...: Without a visible rash and/or break in the skin, the sensation of "itching" is nerve related. Keep track of what may be related to its onset - such as 1) did you eat something that triggered it?, 2) did you wear something that irritated the area?, 3) did you move a certain way that may have aggravated it? DISCUSS with your PCP too - sometimes may be related disease - like diabetes, thyroid, etc.