Praise be to Allah.
Injections that are given to sick people are of two types:
1-Those which contain nourishment. These cause the fast to be invalidated if one uses them deliberately.
2-Those which do not contain nourishment. These do not affect the fast, whether they are given via a vein (intravenous) or a muscle (intramuscular), according to the more correct of the two scholarly opinions, because they are neither food not drink, nor do they take the place of food or drink.
Perhaps this nurse was following the view of those who say that injections break the fast if they reach the stomach.
Whatever the case, the fact that you broke the fast based on his instructions, then made up the fasts that you missed, means that you have done what was required of you, and you do not have to do anything else.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about a woman who dyed her hair then her sister told her that that invalidates the fast, so she broke her fast then made it up. He replied: The answer to this question involves two things, the first of which is this woman who issued a fatwa without knowledge, because if a woman who is fasting dyes her hair, it does not invalidate the fast. The second issue has to do with this woman who received information that was not based on proper knowledge and broke her fast then made it up based on that fatwa. She does not have to do anything now, because she has done what was required of her. End quote from Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen (19/226).
In your question you say: “Fate dictated that…” This is a common mistake, because fate has no will. The correct thing to say is: Allaah willed, or Allaah decreed.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about saying “Circumstances dictated that such and such should happen” or “fate willed that such and such should happen.”
He replied: Saying “fate decreed” or “circumstances decreed” is wrong, because circumstances refers to time, and time has no will. Similarly fate has no will either. Rather the One Who decrees is Allaah, may He be glorified and exalted. If a person says “The will of Allaah dictated that such and such should happen,” there is nothing wrong with that, because will cannot be attributed to fate. End quote from Majmoo’ Fataawa Ibn ‘Uthaymeen (3/113).
We ask Allaah to heal you and give you good health, and to increase you in understanding and knowledge.
And Allaah knows best.