Get this straight: Nobody EVER catches HIV in the environment. Chapped or cracked skin, rashes, etc make no difference.
Look at it this way: Even the busiest HIV/AIDS clinics never have patients who did not have high risk sex or other standard exposures, like sharing drug injection equipment. If exposures like yours could transmit the virus, obviously there would be at least a few patients without the standard risks. But there aren't any.
So you can put aside any and all concerns about HIV except if you have unsafe sex or start sharing drug injection equipment with other people.
Okay I have another question. I have very cracked hands because I don't put lotion on them after I wash them. Sometimes they bleed a little bit and sometimes they don't. My sister came into the house and we walked past each other and I can't remember if I touched her. But I went to the basement and came back up and noticed two different spots on my hands that had a small amount of blood. I washed my hands 10 minutes afterwards but couldn't see where the blood came from and I'm afraid that it must be the blood of my sister. I assume because after I washed my hands there was no blood coming out of my hands afterwards. I'm really concerned because my skin in cracked all over and burns when I put sanitizer on it so they are open wounds. I don't know her status but we don't get along and I'm nervous that I may get an std including hiv.
It seems very unlikely it was blood. But even if it was, there is no risk of HIV or other blood borne infections from this kind of exposure. Don't worry about it.