Since this rash has come back, I would strongly recommend going back to see your doctor
again for a repeat consultation.
It is certainly possible that this is an allergic reaction to a soap or other chemical that you are coming into contact with. However, there are other possibilities as well.
For example, in the summer months, "heat rash" is very common. This is caused by excessive sweating and irritation of the skin leading to plugging of the sweat ducts in the skin. It can be very itchy, but it tends to respond to gentle hygiene and cooling of the skin, as well as avoiding heat and sweating.
It is also possible to have an "allergy" type inflammation of the skin without any specific chemical as the trigger. This is commonly known as "eczema" and it is treated with good skin moisturizing, avoiding of drying agents and hot water, and topical steroid creams.
Finally, there are minor infections of the skin and hair shafts, such as folliculitis, that could present as you are describing.
In short, I'd recommend getting in to see your primary care doctor
right away - they'll help you figure out exactly what is going on and what treatment is needed.