It sounds like you might be dealing with Exercise-induced Urticaria:
Exercise-induced urticaria is a condition that causes hives and other allergic symptoms. It can occur during or after exercise. Hives or "welts" are usually raised, flat bumps on the skin that are more red around the edge than in the middle. Hives may also look like red spots, blotches or blisters. They can occur on any part of the body.
For treatment, the Treament page of the site I linked has the following:
What should I do if I get hives during exercise?
You should stop exercising as soon as you notice the hives. If the hives don't go away in 5 to 10 minutes, or if you have other symptoms, call your doctor right away.
Can exercise-induced urticaria be life-threatening?
In severe cases, symptoms may be life-threatening, but this is very rare. If you ever have severe symptoms, your doctor may prescribe a medicine called epinephrine for you. You inject this medication as soon as symptoms start. It stops the symptoms before they become life-threatening.
Do I have to give up exercise?
You probably don't have to quit exercising. Most symptoms can be controlled by taking the medicine your doctor prescribes and by slowing down or stopping your exercise as soon as symptoms start. You should always exercise with a partner who knows about your condition.
In some people, eating certain foods before exercise may make allergic symptoms more likely to occur. Keep track of what you eat before exercising for a few weeks. If you notice a pattern to your symptoms that seems related to a certain food, stop eating it for a while and see if the hives stop. Also, your doctor may tell you not to exercise for 4 to 6 hours after you eat.
What treatment is available?
Medicines, such as certain antihistamines, can prevent symptoms in some cases. Your doctor can help you identify things that trigger your allergic reaction and prescribe medicine, if necessary. For some people, it may be necessary to avoid certain types of exercise.
So, in short, go see your doctor and they can likely prescribe something for you.