Yes,even if it was used minutes before--the blood on the tip of a syringe is not infectious for the reason i have already explained to you.
It was not a syringe, see a therapist for anxiety issues please.
Even if a syringe is used minutes before?
Even if it was a syringe it still was no risk for HIV transmission because HIV can't survive once exposed to air and therefore it can't infect you.I would stop worrying about this.