I am personally unaware of any reference to the exact scenario you described. Generally, prophets did not turn to music to help make decisions, since they served as the mouth of God. However, music was used "therapeutically" to help sooth distressed individuals:
A prophet of God wrote:But the Spirit of the Lord departed from Saul, and a distressing spirit from the Lord troubled him. And Saul's servants said to him, "Surely, a distressing spirit from God is troubling you. Let our master now command your servants, who are before you, to seek out a man who is a skillful player on the harp; and it shall be that he will play it with his hand when the distressing spirit from God is upon you, and you shall be well." So Saul said to his servants, "Provide me now a man who can play well, and bring him to me." Then one of the servants answered and said, "Look, I have seen a son of Jesse the Bethlehemite, who is skillful in playing, a mighty man of valor, a man of war, prudent in speech, and a handsome person; and the Lord is with him." Therefore Saul sent messengers to Jesse, and said, "Send me your son David, who is with the sheep." And Jesse took a donkey loaded with bread, a skin of wine, and a young goat, and sent them by his son David to Saul. So David came to Saul and stood before him. And he loved him greatly, and he became his armorbearer. Then Saul sent to Jesse, saying, "Please let David stand before me, for he has found favor in my sight." And so it was, whenever the spirit from God was upon Saul, that David would take a harp and play it with his hand. Then Saul would become refreshed and well, and the distressing spirit would depart from him." (I Samuel 16:14-25)
Please note this did involve supernatural intervention, which would not exactly parallel modern times; however, it may help to support your case, if you are seeking to merely demonstrate the historical usage of music therapy, regardless of the perceived illness.
Does anyone else recall some other incident, which would more closely match the one originally described?