"irritating tingling sensation in the skin," also "skin inflammation caused by a burrowing mite," Old English gicce, from giccan (v.) "to itch" (see itch (v.)). Sense of "restless desire" is first attested 1530s; itching in this sense is from mid-14c.
Middle English icchen, from Old English giccan "to itch," from West Germanic *jukkjan (source also of Middle Dutch jöken "to itch," Old High German jucchen, German jucken). Figurative sense of "feel a provoking desire to do or get something" is from early 13c. Related: Itched; itching.