Am I sinful for breaking my fast in Ramadan based on the nurse's advice, knowing that injections do not break the fast?

Injections are of two types: nutritive injections break the fast, while non-nutritive injections do not affect the fast, according to the more correct of the two scholarly opinions. Your breaking of the fast based on a nurse's opinion and your making up for the missed day is sufficient for you, and nothing else is required, as Sheikh Ibn Uthaymeen has ruled. As for the saying "divine destinies willed it," it is incorrect; the correct phrasing is "Allah willed" (شاء الله) or "Allah decreed" (قَدَّر الله), because the will belongs to Allah alone.