Bit of a strange one...and a generic one in there too!
Hello again
You're not being silly but you are wrong.
Alcohol gel will often sting on even mildly damaged skin. There is no relevance in terms of how it might sting on a cut.
The HIV virus is very fragile and is inactivated easily by temperature change and by drying. You are not at risk of HIV from this - even - and its a big even, if he was HIV positive.
I'm going to close this now, ok - but you are safe.