Praise be to Allah.
If the doctor made a mistake in prescribing the medication or in the manner in which it was administered, and the patient died or lost a limb or organ, he is liable and must offer expiation and pay the diyah, unless the next of kin of the deceased lets him off paying the diyah. And there is no qisaas in this case, because his wrongdoing was not intentional.
In the answer to question no. 114047 we discussed cases in which the doctor is liable, among which are the following:
“2. Treatment by one who is ignorant; because of his ignorance he is regarded as having transgressed, and the hadeeth quoted above states that he is liable.
“Ibn al-Qayyim (may Allah have mercy on him) said: According to sharee‘ah, the ignorant doctor is liable. If he deals with medicine and practices medicine without any previous knowledge thereof, then he is causing harm and death because of ignorance, he is being negligent by practising that of which he has no knowledge, and he is cheating the sick person, therefore he must be liable.
“… 4. If a skilled doctor makes a mistake in prescribing treatment: likewise the skilled doctor is liable if he tries to work out the best prescription for treating a patient, but he makes a mistake, and the treatment damages a limb or organ, or kills the patient.
“5. The skilled doctor who does something that other doctors of this specialty do not do: this refers to a doctor who overstepped the bounds as established by the medical profession or falls short in diagnosis.” End quote.
In light of what you mention of the possibility that the patient died because of the way the painkiller was administered, we think that you should present this question in detail to three trustworthy doctors who are specialized in cardiology. If they agree that the way in which the painkiller was administered was the cause of death – as appears to be the case – then you are liable [i.e., you must pay the diyah and offer expiation]. Otherwise you do not have to do anything, because the basic principle is that you are free of blame.
See also the fatwa of the Standing Committee (Fataawa al-Lajnah ad-Daa’imah, 25/81).
If these doctors determine that you caused the patient’s death, then you have to look for the family of the deceased and tell them, and it is up to them whether to demand the diyah or let you off. However, this diyah is not due from you; rather it is due from your ‘aaqilah (male relatives on your father's side). If you do not have any ‘aaqilah, or if they refuse or are unable to pay, then the ruling is to be decided by the qaadi (shar‘i judge).
With regard to the expiation, it is fasting for two consecutive months.
And Allah knows best.