I've been having itching on the soles of my feet, the palms of my hands and now my scalp is itching. no sign of any rash, bumps or anything visible.

Itching palms/soles: Usually, the first thing we think of , if it is new and sudden onset - with palms and soles involved, is a drug allergy. Usually with a rashl. Any new medications? IF it is chronic- and the skin peels it could be dyshydrotic eczema. This generally responds well to steroid creams and ensuring skin is not overly moist ( i.e. sweating in socks). This type of eczema is usually between fingers/toes.