Whilst in hospital, after surgery a nurse tried to inject me without waking me up, it scared me a a lot, the lights were dim ~& the nurse wore dark clothing & she was black. There was no time to think about what was happening, but she quickly reassured me that she was just giving a scheduled jab, not realising I was asleep.I don't think it's possible to give a jab without waking the patient up. For me at the time I imagined that 'The Grim Reaper' had called. We became friends!
If we're talking from a fictional point of view (like a movie or book) sure, someone could do that. It would depend on how heavy a sleeper you are. I think I would wake up, but I'm not sure my boyfriend would. I have heard horror stories in the news of certain crazy people intentionally infecting others with HIV or other diseases. If you looked around the internet you might find something. I am almost completely sure this will never happen to you though.
Your post is very similar to one I already answered by someone else. Yes, I believe that you would be woken up if somebody stuck you with a syringe. Why would somebody do that anyway? You are stuck on this irrational thought and you need to find a way out of this cycle.
You can always make a doctors appointment and discuss this when him/her. That way, if you have any area on your body you are concerned about or just the fact that you are thinking this thought, they can do the proper tests and/or point you in the right direction to take care of your anxiety over this.
I do not believe you have anyting to worry about.