Maybe, and maybe. Not enough information to answer either question.
I believe the "pneumonia diagnosis" was 9/2, not 9/9, implying nine days of Rx before the 9/11 event. If that's true, I would not expect her to be contagious (and many forms of pneumonia are not).
Beyond all that - you have a woman with a chronic cough, who has been carried with a diagnosis of "allergies". Hopefully, there's a negative chest x ray at some point to support that diagnosis, but we don't know. NOW, your "allergies" patient has no only a chronic cough, but an abnormal chest X ray.
Step one, with regard to the X ray, is to treat with antibiotics and hope the abnormality goes away.
Along with the antibiotics comes a diagnosis of "pneumonia". Remember, the government no longer allows "rule out" or "suspicion of" as diagnoses, or as justification for tests.
It's much too soon to evaluate the care HRC has been getting, but, like any other sociopath and congenital liar, it's possible she's been fool
"like any other sociopath and congenital liar, it's possible she's been fooling her doctor".