actually the term for hospital acquired infections is nosocomial. Iatrogenic means caused by the treatment or error in the treatment and can refer to infections as well as other complications.
You live and learn. That is the first time I have ever heard of “nosocomial” infections.
I had an aunt who drove the doctors to distraction with persistent infections after hip replacement. It was finally tracked down to a low level dental infection, and one less tooth later, her hip finally healed.