This seems to be a very irrational fear. An anxiety fear. Why do u have this worry in the first place? But to answer your question. I highly doubt it. Have you ever had blood drawn? Or an IV in you? It's not a pleasant feeling
You fear being injected. So I doubt that you would be able to sleep through it, even if you are in a deep sleep. You would feel it and suddenly wake up because you're hypersensitive to that fear. Like a mother is hypersensitive to the sound of her baby's cry. She can wake from a deep sleep even when she's sleep deprived and running on empty whenever she hears the slightest cry from her baby. I understand your situation. I have irrational fears too. Logically I know the truth but yet somehow I wonder "well, what if?" The best advice I can give you is to confront the fear with the truth. Then keep on telling yourself the truth every time you start the what if thinking. Keep on telling yourself those truthful statements (even if you still feel the doubts) until you start to believe the truth. It's like you're stuck in a rut that your thoughts have replayed over and over. It takes time to re-grove a new thought.