Can you get hiv from broken needle. I mean to say only the metal needle which is broken from its plastic part.
A really key part to your post is "I couldn't find any". What is the talk of a broken needle that you never could find? Would it magically just disappear? No. So, no needle poked you, no broken syringe was there, this scenario is coming out of your imagination. And your imagination is very anxious it would seem. Furthermore, you are correct that it's not 'just being poked' that transmits HIV. HIV is inactivated by air. So, any needle tip or syringe piece would be exposed to air. Injections are where there is any potential.
The only way adults get HIV is from unprotected vaginal or anal sex or sharing IV drug needles as in injecting with them.
Anxiety is something you can talk to your doctor about to get help.
Firstly, you are not going to get infected in the way you have described, there is no scope of transmission. Unless you were injected with infected fluid into your body there is nothing to worry.
Secondly, you seem to be paranoid about this event, it is not logical for you to think that a student would be such vindictive. This entire idea of your student procuring infected fluid on a needle from some place he knows and pricking you with it is irrational. You might want to see a counselor to address these issues.
This is not a rational question. It's the type of question that only someone with severely irrational HIV phobia would ask. This is not an HIV problem, it's a mental health issue. Please see a therapist for your out of control thinking.