I have the same situation. western medicine call it "exercise in

There is no effective medicine to prevent the itchy. I had this since I was a teenager. On the way to school, I would stop walking and scratch myself. It becomes worse now, even when I'm not exercising, the itchy could come any time. I call it "itchy attack". The reason behind is your skin can't effectively adjust body temperature through sweating while exercising, toxic substance that are normally excreted through sweating are retained in blood and causing itchy. When you scratch yourself, being the skin is super sensitive, it becomes red and swollen immediately. Pores are open, heat and toxic substance are out and immediately relieve itchy even though the relieve is only temporarily.

i found dry sauna helps a lot. Whenever I'm having an itchy attack, as soon as I walking into a sauna room, my skin gets calm down, pores are open immediately. After sweating a little, I then go to gym. Try to avoid AC while exercising, it closes pores