Is the brother who took a portion of the financial aid designated for his sick relative to pay off a debt of his own, claiming that the sick person does not need the full amount and that he himself is in financial distress, sinful?

Your brother is not permitted to take anything from the charity entrusted to him for delivery to the patient. His need and debt do not justify betraying the trust, for he is merely an agent, and has no authority to dispose of the charity except as authorized by the donating party.