Praise be to Allah.
We ask Allah, may He be exalted, to have mercy on your father and forgive him, and to console you and grant you an immense reward.
With regard to this matter, you should consult doctors to find out whether death resulted from your actions or not.
If three trustworthy doctors say that the cause of death – as appears to be the case – stems from the air getting in through the injection, then you are liable. What liability means is that you must give the diyah (“blood money”) to the heirs of the deceased, unless they pardon you. And you must offer expiation, which takes the form of freeing a slave. If this is not possible, then you must fast for two consecutive months, because Allah, may He be exalted, says (interpretation of the meaning): “And never is it for a believer to kill a believer except by mistake. And whoever kills a believer by mistake - then the freeing of a believing slave and a compensation payment presented to the deceased's family [is required] unless they give [up their right as] charity. But if the deceased was from a people at war with you and he was a believer - then [only] the freeing of a believing slave; and if he was from a people with whom you have a treaty - then a compensation payment presented to his family and the freeing of a believing slave. And whoever does not find [one or cannot afford to buy one] - then [instead], a fast for two months consecutively, [seeking] acceptance of repentance from Allah . And Allah is ever Knowing and Wise” [an-Nisa’ 4:92].
The diyah must be paid by your ‘aaqilah (male relatives on the father’s side), and you should not take any part of it.
For more information on the testimony of three doctors, please see: Fataawa al-Lajnah ad-Daa’imah (25/80); Fataawa ash-Shaykh Muhammad ibn Ibraaheem (11/254); and the answer to question no. 175020 on our website.
For more information on what is meant by the ‘aaqilah (male relatives on the father’s side), and what may be done if there is no ‘aaqilah or they refuse to pay the diyah, please see the answers to questions no. 52809 and 175020.
If the doctors say that air bubbles getting into the injection was not the cause of death, then you do not have to do anything.
And Allah knows best.