Itchy Skin and Swelling During Exercise

Whenever I exercise, my entire skin gets extremely itchy. After a few minutes of this, some parts of my skin; such as my elbow and face area, will swell up in white blotches. While all of this is going on, I feel a very strong heat and sweat intensely. It usually take around 30 minutes of me enduring the overpowering itch all over my body until it finally goes down. Cold showers usually help but I haven't tried any medication aside from antiallergic. I've had this problem since puberty and it's only been getting worse. I still have no idea what it is and it is a very strong deterrent from exercising.