Hives and Exercise

I have been diagnosed with autoimmune thyroiditis and take a thyroid supplement every day along with an antihistamine for hives. I am not allergic to anything, it just my body reacts when I exercise, sweat, heart beats rapidly, or when there is a sudden change in temperature. I really want to exercise to help increase my weight loss. Can someone please help me? I want an exercise routine that I can get through without getting hives.

Thanks.
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