Can you get hiv from feces touching cuts on fingers?

I have a couple open cuts on my hands and I was having bathroom issues in the bathroom(sorry this is very tmi and gross but idk where else to go to ask this) so i stood up to wipe but the toilet automatically flushed so it scared me then I look around and realized i stepped in a piece of poop and it smeared. I'm pretty sure it was mine, because I didn't see it when I went into the stall.So then I proceeded to wipe it up with toilet paper. Now I am worried that if poop came into contact with one of the small cuts on my hand(one of them probably got really close to the poop, but it is really small but still) if it was from an hiv positive person and it came into contact with my cut, could I get hiv from it? What is the poop happened to have blood in it? I know hiv dies in the air, but if it was inside the poop wouldn't it not be exposed to air so it wouldn't die? Please help I'm really worried.