The subconscious mind is thinking. You have to believe that your fears are irrational and have to accept the fact that no one has tried to deliberately given you HIV. That's when your mind will stop playing tricks.
I suggest you take this to anxiety forum. Or perhaps seek help from a professional if your anxiety is persistent. I repeat, HIV is not your problem. All is well.
Your thoughts are irrational. No one at a healthcare setting would infect you intentionally. They are trained professionals who handle blood tests all the time, they are very careful in handling needles.