I went to a hospital to have blood drawn once upon a time. The phlebotomist was telling me it was the end of her shift – she was about to go home but her boss made her stay to take my blood. She said she’d felt awful all day. She coughed into her hand a half a dozen times during the procedure. I asked her, as nicely as I was able under the circumstances, “Please don’t do that while you are opening up my vein.”
And that was completely intentional. Enjoy.
Why not cover your nose? Because you can not get any distance that way at all.