I've had poison ivy and can't imagine it on my privates! And you say this is worse!! Yikes. Have you ever seen a dermatologist? I'm sure you don't relish the thought of getting this looked at when active but you should. It could be something like ezcema. (also called atopic dermatitis). Psoriasis is another skin condition that can cause chronic itching in that area. Sweat could actually irritate you and cause it, believe it or not (ever try Gold Bond which you sprinkle right on there?). https://my.clevelandclinic.org/health/diseases/12324-sexual-health-genital-itching
Have you eliminated things like the soap you use or laundry detergent (granted, the laundry detergent would be unlike to only cause itch on your genitals).
I would sincerely consider seeing a dermatologist to get an answer on this and hopefully, an easy solution.