Hello,
Thank you for asking your query at DoctorSpring.
It seems that you have a condition called Sweat Hypersensitivity and/or mild Cholinergic Urticaria. This is caused by body's own reaction to sweat and heat. The confirmed diagnosis require some specific tests and you should get in touch with an Allergy and Immunology specialist for that purpose. (Allergen test).
Avoiding sweating is an obvious solution, but of course is not always practical. You can try taking an anti allergic medication like Allegra when you expect such a situation and see whether there is a response. Definitive treatment depends on a conclusive diagnosis.
Hope this helps
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Thank you