Welcome to the forum.
There is no risk of HIV or any blood borne infection from these events. Even if the nurse's glove indeed contacted the blood, and even if that blood were infected, the alcohol wipe would have instantaneously inactivated any virus present; a little blood on the band-aid would not be able to transmit infection through a needle wound; and it is difficult to imagine that the nurse touched the needle through which your blood was drawn.
It is probable that nobody in the world has ever acquired HIV or viral hepatitis from an exposure like this, and to my knowledge there have been no HIV transmissions to patients by medical procedures in the US or other industrialized countries since the blood-borne nature of HIV was recognized and people stopped re-using injection and blood drawing equipment.
So no worries, no need for testing, and if you have a regular sex partner, you can safely continue your normal sexual practices.
Best wishes-- HHH, MD
It is unlikely the nurse would touch the needle; if he did so accidentally, he would change the needle before injecting you; and even if none of that happened, the risk of HIV transmission would be exceedingly low.
These fears are irrational. Do you really think you might be the very first person to catch HIV in this manner, among the billions in the past 30 years who have received injections or had blood drawn in emergency rooms?
Don't overthink it. Do your best to move on with your life without worry. I won't have any further comments or advice.
Thank you for your answer. I'm a little bit confused by "it is difficult to imagine that the nurse touched the needle through which your blood was drawn". Do you mean that the nurse would not touch the needle before giving me the injection for certain? If he touched the needle accidentally, which is possiable because he was holding the injector while he was sterilizing my skin, and contaminated the needle, am I at risk?