So a nurse is a "honey sister" in Ukrainian? :D Or rather something like a "med(ical) sister" I guess? Anyways, it's a good mnemonic.
Yes, it is a contraction from "medical sister" :) And you can call them with the full term, but it is very long, so shortened form is much common. But official name of the position is the full one.
Is it used for both women and men?
Well, man is obviously not a "sister" :) It is "медбрат" (the same logic here)