Since the red rash
is around mole, so it can be due to contact dermatitis, allergic reaction or heat rash. Take some Benadryl after consulting your doctor, use mild soaps like Dove and apply some calamine lotion on the rash. Also wear cotton clothes.
If however you notice changes in the mole's color, height, size or shape, you should have a dermatologist evaluate it. You also should have it checked if it bleeds, oozes, itches, appear scaly, or become tender or painful.