It sounds like your relative is suffering from thyroid disease and that her meds to be adjusted. That could account for hoarseness, loss of hair, very dry skin, achiness, and her TSH being a .51, entirely too "high" (ideal levels are between 2.0 and 7.0). The scarring on her legs certainly sounds like psoriasis, but it could also be discoid lupus, a different manisfestation of the lupus disease. It's worth taking her to see a rheumy to get some more specific blood tests done.
Psoriatic arthritis usually has these symptoms: swollen fingers but not hands (sausage fingers), swelling around joints, fingernail pitting, swelling in the sacroiliac joint, pain upon waking that usually eases as teh day progresses, etc. It sounds more like your relative might need to see an endocrinologist to get her thyroid back in order. Good luck
She might want to get a 2nd opinion to see if she can get a diagnosis of psoriatic arthritis or Lupus or ?. If they can formalize a diagnosis she can get on some other meds to suppress her immune system and hopefully stop any of the disfiguring issues.