I always am surprised at the level of HIV knowledge out there about what would be a risk. Hands do not transmit HIV (if it did, think of how many people would have it). The only risks for HIV are to have unprotected vaginal or anal sex or to share IV drug needles. Air inactivates the virus. So you could never get HIV through a hand shake even if the other person was bleeding (if they wrote to us about the hand shake from their side of things, we'd tell them no risk as well.) I would not assume your friends have HIV either.
HIV is not transmitted through handshakes: that's something they teach at school, right?
Skin on your hands is quite thick and eczema patches don't make any difference. You are safe.