The feet and hands
are worrisome, as these can be symptoms of diabetes
Especially if there is no rash.
IF you have been tested for that, and came back negative, then I would start looking at things like hand,foot, and mouth disease, eczema, psoariasis, allergies, dry skin, nerve damage, and other much worse problems. Because you said it's under the skin, it sounds more like a nerve condition.
There are so many things that it could be, and without testing it may be hard to figure out.