@Littlescared,
You are compounding a series of extremely unlikely events on top of each other. Your friend is unlikely to have HIV. If they did, it is likely under treatment and not very transmissible. If it was, it is unlikely the kitten broke her skin. If she did, it is unlikely a miniscule amount of blood contained enough active virus to infect you given that mosquitoes don't carry HIV. You are fine.
That said, cat scratch fever is a real thing and you can get sick from cat scratches but it has nothing to do with your friend's profession.