This kind of rash which comes and goes can be due to hives. Hives (medically known as urticaria) are red, itchy, raised areas of skin that appear in varying shapes and sizes. They have a tendency to change size rapidly and to move around, disappearing in one place and reappearing in other places, often in a matter of hours.
So please get this possibility evaluated.
Till then, give some antihistaminic like Benadryl and apply some calamine lotion. If the symptoms persist then please get an evaluation done by a dermatologist. He may need topical and oral steroids.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your dermatologist. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.