Praise be to Allah.
In the answer to question no. 50555, we explained that sickness is one of the excuses that makes it permissible not to fast. Also, if a sick person requires treatment during the day in Ramadan, it is permissible for him to break his fast and make up the days when he did not fast later on. Based on that, if fasting will be harmful to this girl, or it will exacerbate her sickness, there is nothing wrong with her mother giving her daughter medicine during the day in Ramadan, but in this case she has to convince her daughter that it is permissible for her not to fast, because she is sick, and Allah, may He be glorified and exalted, by His mercy has excused the sick person from fasting, as He says (interpretation of the meaning): “and whoever is ill or on a journey, the same number (of days which one did not observe Saum (fasts) must be made up) from other days” [al-Baqarah 2:185]. There is nothing wrong with making her complete the fast, so long as she makes up that day after Ramadan.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him) was asked:
I have a mental illness, and when I went to the doctor, he gave me pills which I have to take for five years, one pill every twelve hours. What should I do, especially during the day in Ramadan, because now the fast lasts for fifteen hours, and if I delay taking the pill even for one hour, this sickness will come back to me and I will have seizures?
Allah, may He be glorified and exalted, says (interpretation of the meaning): “So keep your duty to Allah and fear Him as much as you can” [al-Taghaabun 64:16]. If sickness will result from delaying the dose until after its usual time, then there is nothing wrong with breaking the fast, if the day is long, and the fast is fifteen hours. On such days, there is nothing wrong with taking the pill that has been prescribed by the doctor, and breaking the fast by doing so, then refraining from eating and drinking for the rest of the day, and making it up later on, because breaking the fast is done for that purpose. So he may break the fast, then refrain from eating and drinking, then make up the day later on. But if it is possible to delay the dose without any hardship, then he must delay it so that he can take the dose at night.
End quote from Fataawa Noor ‘ala ad-Darb (16/130)
For more information, please see the answer to question no. 97798
What you mentioned about that girl being keen to do acts of worship and loving to do good, despite the illness that she suffers – should motivate you to be keen and hasten to do good, because shortcomings in one who is capable are not like shortcomings in one who is not capable. Shortcomings in one who is capable are regarded as faults, as someone once said: I have never seen any faults in people like the shortcomings of those who are able to do things properly.
May Allah help us and you to obey Him and hasten to do so, and may He decree a speedy recovery for that woman, for He is able to do that.
And Allah knows best.