Referred itch

About one person in four or five is conscious that scratching an irritation may produce an itch elsewhere. The sensation is well localised, comes and goes quickly, and recurs (occurs) when scratching is repeated a short while later. Scratch and referred itch are ipsilateral (belonging to or occurring on the same side of the body); scratching the site of the referred itch does not cause the original spot to itch. Scatching face, palms, or soles does not produce referred itching. Different people stimulated in the same region do not necessarily feel referred itch in the same place. The mechanism of the phenomenon is unknown, though it may be thalamic.

Br Med J 1976; 2 doi: https://doi.org/10.1136/bmj.2.6040.839

Why Do I Sometimes Scratch One Body Part and Feel It on Another?

Lots of people report feeling a sensation from a scratch in places far from where they’re scratching.
English clergyman (牧師)/scientist Stephen Hales first described the phenomenon in the 1730s, referring to it as “instances of the sympathy of the nerves.”
For most people, referred itch is just a weird annoyance. It doesn’t do any damage or have any ill effects, and so it doesn’t get a whole lot of research attention.
One idea is that referred itch is the product of our complex system of nerves being “rather irregularly distributed” throughout the body.
It could also be that the mix up isn’t in the nerves, but the brain.

Source: mentalfloss.com