What must I do after committing a medical error that resulted in the patient’s death? Should I inform their family? Am I liable for the blood money (diyah), and how can I pay it without their family knowing?

If you caused the death of a patient out of ignorance, you must repent to Allah, and you must pay the blood money (diyyah) for the deceased, which you and your 'aqilah (male relatives on your father's side) should pay to his family. This is based on the Prophet's (peace be upon him) saying: "Whoever practices medicine without having been known to practice it before is liable." The blood money can be delivered to the deceased's family through a stratagem if you fear harm.