Yep, like aceplace57 says, plague doctors wore masks like this to protect them from the “bad air” which was thought to spread sickness, following the Miasma theory of disease. This was replaced by germ theory in the 19th century. It’s easy to see how the mask would offer some incidental protection from the microorganisms, even if the logic behind them was flawed.
I think the future doctor could avoid the risks of pretending to be some kind of wizard and instead build off Miasma theory by a few simple experiments to prove to the powers that be that germs/viruses were responsible, leading to proper prevention methods.
Louis Pasteur was able to prove microorganisms existed in the air using glass flasks and beef broth.
*The argument continued into the nineteenth century, when the German scientist Rudolf Virchow in 1858, introduced the concept of biogenesis; living cells can arise only from preexisting living cells.
But the matter remained unresolved until two years later when the great French scientist Louis Pasteur, in a series of classic experiments demonstrated that (1) microorganisms are present in the air and can contaminate solutions; and (2) the air itself does not create microbes.
Pasteur filled short-necked flasks with beef broth and boiled them, leaving some opened to the air to cool and sealing others. While the sealed flasks remained free of microorganisms, the open flasks were contaminated within a few days.
In a second set of experiments, Pasteur placed broth in flasks that had open-ended, long necks. After bending the necks of the flasks into S-shaped curves that dipped downward, then swept sharply upward, he boiled the contents. The contents of these uncapped flasks remained uncontaminated even months later. Pasteur explained that the S-shaped curve allowed air to pass into the flask; however, the curved neck trapped airborne microorganisms at the bottom of the curve, preventing them from traveling into the broth.*
So basically, just accelerate the timeline that led to germ theory (a microscope would be helpful, but not required, IMO). Prove it to the powers that be, then open a savings account before coming back to the present.