I am thrilled to know that after at least 10 years of experiencing this excruciating itchiness during any cardio. workouts and 10 years of doctors telling me over and over that it was my laundry soap or stress or dry skin and me knowing that it wasn't any of those things, that finally I have an answer and know that I am not alone.
If you check on Wikipedia, and do a search for 'extreme itchiness during exercise', that it should come up with a known condition, the treatment for which is the use of anithistamines. However, it notes that this condition, untreated, could lead to shock, anaphalaxes and possibly death so I will be going back to, another, doctor with the information in my hands to get more information.
I have noticed that slowly building up my running time, vs. walking time, results in my being able to run longer without the itchiness until eventually it goes away, except in the winter. I run indoors in the winter to avoid the extreme temperature changes.