Praise be to Allah.
Do nose drops break the fast?
If the nose drops do not reach the throat, they do not break the fast. But if they do reach the throat, then they do break the fast.
Cannot do without nose drops in Ramadan: What to do?
If the nose drops reach the throat, in the sense that the sick person can detect their taste in his throat, and he is not able to do without them during the day in Ramadan, and he does not have any suitable alternative, and his sickness is one from which there is no hope of recovery, then in that case he comes under the same ruling as an old man (who is unable to fast), and he has to feed the poor only.
Allah, may He be exalted, says (interpretation of the meaning): “And as for those who can fast with difficulty, (e.g. an old man), they have (a choice either to fast or) to feed a Miskin (poor person) (for every day)” [Al-Baqarah 2:184]
Ibn Qudamah (may Allah have mercy on him) said:
“In the case of the sick person who has no hope of recovery, he may not fast and should feed one poor person for each day, because he comes under the same ruling as an old man.” (Al-Mughni, 4/396)
Ruling on consuming something that breaks the fast due to ignorance
With regard to the days you have fasted in the past, then we hope that by the grace of Allah that will be accepted from you, and you do not have to do anything, especially since you used those nose drops when you were unaware that they break the fast; moreover this ruling is one concerning which there is a difference of opinion among the scholars.
The correct scholarly view is that if a person does one of the things that break the fast not knowing that it breaks the fast, he does not have to do anything.
We ask Allah to grant you a speedy recovery.
For more, please see these answers: 80208 , 232563 , 156278 and 188934 .
And Allah knows best.