Hi, welcome to the forum, sweating is known to cause allergic manifestations in certain individuals and can worsened with concomitant Atopic dermatitis or Contact dermatitis.
Usually allergens are small molecules which can penetrate the layers of the skin and sweating is known to enhance this action.
Topical lotions such as calamine decreases pain and pruritus. Systemic antihistamines (antipruritics) such as hydroxyzine or cetirizine against prescription may be helpful. Even addition of corticosteroids has possible benefits.
Talcum, Aluminum Chloride with Ethyl Alcohol, Anticholinergics or Propantheline Bromide at bedtime can be used against prescription. The actual treatment would be avoidance of the primary allergen.
I suggest you to consult dermatologist for further evaluation and treatment. Take care and regards.