Dry, dark patch of skin that sometimes burns and has been there forever

Might be Venous Stasis. I had it recently, and I have hypothyroidism as well, and your age too! (though I think that's unrelated.) It's essentially a blood clot from sitting still for too long. It starts off looking red, but turns into a dark spot that will fade over time. On me, the skin was very itchy, sometimes hot, and very dry. You seem to have all the symptoms as me, except that it lasted 10 years. Mine only lasted half a year/year, max. There might be a chronic variation. The images on google are so extreme in their examples, be warned. This is essentially what mine looked like (https://i.imgur.com/sYz9Ncz.jpg) veins excluded, and it slowly over time, discolored from red to a dark patch.

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