Did see a mom once who the answer for this was topical allergy, and after using non allergenic detergent, double rinsing clothes with vinegar and using no products on her nipples, it went away. However, she had more of a 'shards of glass' feeling than a burning feeling, and her breast skin was reddened. So I don't know if this could apply in your case.  Yes, a Dermatologist would probably be helpful. 
Mary Taylor, LLLL, IBCLC 

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