Do the symptoms the husband is experiencing—shortness of breath and pain between the shoulders—which disappear when the Quran or Adhan is recited, and which began after his financial situation improved, and for which hospitals find no explanation—are these considered envy (hasad), sorcery (sihr), the evil eye (ayn), or an organic illness?

There is nothing definitive in the interpretation of what you mentioned. The husband is advised to fortify himself with divine protections, maintain the morning and evening remembrances (adhkar), recite the Qur’an, and Surat Al-Ikhlas (definition) and the two Mu'awwidhat (Surat Al-Falaq and Surat An-Nas) three times in the morning and evening. He should also regularly perform four rak'ahs of prayer at the beginning of the day, and repeat "Hasbi Allahu la ilaha illa Huwa, alayhi tawakkaltu wa Huwa Rabbu al-arshil-azhim" (Sufficient for me is Allah; there is no god but He. In Him I have placed my trust, and He is the Lord of the Mighty Throne) seven times in the morning and evening, and perform legal ruqyah (definition).