Are rheumatologists familiar with the diagnosis and treatment of lyme disease and its co-infections? if not, who treats these tick-borne infections?

Yes, but . . .: Acute lyme disease is a well recognized problem with a fairly straight forward medical approach. In that case a rheumatologist or even a general physician should be able to manage it. If you are speaking of "chronic lyme" the story is different as the syndrome is still not recognized as a distinct clinical condition by mainstream medicine. Consider a holistic md to evaluate this.

Infectious Diseases: Certainly a rheumatologist can treat lyme, but in complex situations, not only can a board certified infectious disease specialist an treat lyme, they can order appropriate tests to diagnose and then treat co-infections such as anaplasmosis, babesiosis, and erlichiosis. In addition, they may be able to determine if the illness you is due to something other than a tick-borne illness.