I'm a medical student (studying to be a physician) and I have never heard "infectiologist" used. In the United States at least we say "infectious disease specialist." Among physicians there is also the abbreviation "ID," so for example one could say "he's an ID specialist" or "an ID doc." These are too informal for writing, of course.
I have heard "infectology" when talking about the study of infectious diseases, but even in medical dictionaries there is no such word as "infectologist" or "infectiologist."
I myself wish to be an infectious disease specialist!