Thanks for the question. It is hard to be certain without seeing the actual brown spots, but from the description, it does suggest that this is post inflammatory hyperpigmentation (PIH).
PIH is pigmentation following inflammation of the skin from various causes such as eczema, psoriasis and trauma. In your case, with the history of dry and itchy skin, preceding eczema seems likely. The brown spots of PIH are not permanent but may take week or months to gradually settle. In the meantime, moisturize the skin regularly and avoid scratching it. The important thing is to prevent the eczema so that you will not leave new marks.
If not better, you should consider seeing your doctor/dermatologist to confirm the diagnosis and treatment.
