When I exercise hard, I sometimes get a fine rash on my arms that itches. Taking an antihistamine can help.
"During exercise, histamines are released. Histamines are proteins involved in autoimmune responses like an allergic reaction to pollen or dust. People who are sensitive to histamines can experience rashes, itching, and other allergic symptoms during exercise just like you are describing. Most of the time, the rashes appear on the chest and thighs, but they can appear on the neck or arms, too. Sometimes exercise also reacts with food allergies or medications (for example, antibiotics, pain medications, sedatives, tranquilizers, and diuretics) to cause the problem. The problem typically occurs more in cold weather than warm."