Nick, you do not need anyone else to tell you that you didn't have a cat in hell's chance of becomeing infected from the scenario you describe. Hiv simply doesn't operate like that. Routes of transmission are from immediate body to body contact through the bloodstream or mucous membrane. That is why sharing needles, having unprotected intercourse (anal, vaginal and very very rarely oral), occasionnally breastmilk intake are the only documented cases of hiv transmission.
Plus, I strongly doubt any blood contact was made between you and the other patient. Certainly not any sufficient amount to sustain the hiv virus on the journey to your arm, where I suppose you think it might 'jump' its way into you? Impossible.
Let me tell you, if hiv was as easy to infect as the situation you describe, the majority of the world's population would be hiv
so, to conclude, you do not have hiv from this episode. Ok?