No risk , hiv need unprotected anal , vaginal sex (penetrative)
As it is weak in environmental conditions ,it need close intact exposure that hapoens in sex
Your exposure is no riski
theres no risk for the event u mentioned,risk for infection are unprotected anal or vagina sex with some one known with hiv.
You had zero risk. Only sex risks are unprotected vaginal or anal and you were a long way from that. You can't get HIV from a finger cut or any cut so you should stop examining your finger and get back to your normal life.