He cannot do without nose drops in Ramadan

Firstly: 

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. We
have discussed this previously in the answer to question no.
93531

Secondly: 

If these 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, because 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 Miskeen (poor person) (for every day)”
[al-Baqarah 2:184].

Ibn Qudaamah (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.

End quote from al-Mughni, 4/396 

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. 

That has been discussed previously in the answer to question
no. 93866 

We ask Allah to grant you a speedy recovery. 

And Allah knows best.