Praise be to Allah.
Treating sickness with costus is a beneficial prophetic remedy. Al-Bukhaari entitled a chapter in his Saheeh: Chapter on treating sickness with Indian costus or sea costus, in which he quoted the hadith of Umm Qays bint Mihsan, who said: I heard the Prophet (blessings and peace of Allah be upon him) say: “You should use this Indian incense, for in it there is healing for seven diseases: it should be administered through the nose for swelling in the uvula, and administered to the side of the mouth for pleurisy.” Narrated by al-Bukhaari (5692) and Muslim (2214).
Deliberately inhaling smoke and incense breaks the fast according to a number of fuqaha’. This is the view of the Hanafis and Maalikis, and is mentioned in fatwas by Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him). That is because incense has tangible, visible particles which, if a person inhales them, will enter his nose and then reach his stomach.
Ibn ‘Aabideen said in his Haashiyah (2/97): The words “if he lets the smoke reach his throat” mean no matter how that is done; if he perfumed himself with incense and brought it close to himself, and inhaled it, knowing that he is fasting, then he has broken his fast, because it is possible to avoid that. This is a matter concerning which many people are heedless. End quote.
Ad-Dardeer said in ash-Sharh al-Kabeer (1/525): One should not let the smoke of incense or the steam from a cooking pot reach the throat, because once it reaches the throat, making up the fast becomes obligatory.
Similar to that is smoking through a water pipe and the like, because it reaches the throat and in fact reaches the interior part of the body (jawf). This is unlike smelling the fragrance of incense and the like without letting the smoke reach the throat; that does not break the fast. End quote.
In fact, al-Bahooti and other Hanbalis clearly stated that deliberately letting the smoke reach the interior part of the body breaks the fast. He said: If smoke reaches his throat without any deliberate action on his part, that does not break the fast because it was not done deliberately…
From this it is known that the one who deliberately inhales the smoke has spoiled his fast.
End quote from Kashshaaf al-Qinaa‘ (3/370); see also: Haashiyat ar-Rawd by Ibn Qaasim (3/402).
It says in al-Mawsoo‘ah al-Fiqhiyyah al-Kuwaitiyyah (26/210): The Hanafis and Maalikis are of the view that if the fasting person deliberately lets the smoke of incense reach his throat, and he smells its fragrance, he has broken his fast, because it is possible to avoid that. If it does not reach his throat, it does not break his fast.
But if he smells air in which there is the fragrance of roses and the like, that has no particles, then he has not broken his fast according to the Hanafis, although that is makrooh according to the Maalikis.
Similarly, it is makrooh according to the Shaafa‘is to smell fragrant plants and the like during the day for the one who is fasting, because it is a kind of luxury. Hence it is Sunnah to refrain from doing that. According to the Hanbalis, if perfume is in the form of powder, it is makrooh to smell it, because there is no guarantee that the one who smells it will not bring it to his throat. Hence it is not makrooh to smell roses, amber and musk that are not in the form of powder. End quote.
What is most likely to be the case is that if you bring the smoke of costus close to your nose and inhale it, it will reach your throat. Hence if you want to use it, you should do that before Fajr or after Maghrib, and that will be sufficient. In sha Allah.
And Allah knows best.