When I read this I feel very bad for you. Your anxiety is overshadowing your life. Why are you taking another HIV test? Unless you have had unprotected vaginal or anal sex or shared IV drug needles, that is unnecessary. Testing over and over is just part of your anxiety. And then the fear once you've given into the anxiety enough to test again about needles that is clearly irrational when they even allowed you to select the unopened needle should indicate to you that this is not a minor problem. Do they have the specialty of psychiatry where you are located in the world? These are doctors that specialize in mental health issues like anxiety and obsessive compulsive disorder (and your phobia, as you call it). Anxiety and OCD are treatable disorders. I hope you take our advice so you don't have to deal with this fear so frequently.
You said yourself that you chose a new needle that she opened in front of you. It's clear that you're suffering from irrational health anxiety. You don't need help for HIV but you do need to seek therapy to help you overcome this mental problem.
Since you chose the needle that wasn't opened but now are afraid that you didn't choose it, your situation is a mental health issue. No one here can convince you that you chose it so you need to see a mental health therapist to try to help you.
You had no risk of hiv, so that is all anyone can tell you.