Your severe, bleeding hand rash is likely linked to your recent thyroid diagnosis, which can cause extreme dryness. For relief, frequently apply a thick emollient like plain white petrolatum and wear cotton gloves at night. To treat the painful, bleeding areas, you need a prescription topical corticosteroid ointment (such as triamcinolone acetonide) to reduce inflammation and heal the skin. Avoid harsh soaps and limit contact with hot water. Since you have pulmonary hypertension and open skin lesions, please consult your healthcare provider or a dermatologist promptly for a precise diagnosis, prescription treatment, and to prevent any infection.