The new etiquette? I don't believe that the practice is new at all. Haven't we all seen others do it, or have been guilty of doing it ourselves? :

Sneezing and coughing into your sleeve helps prevent airborne transmission of viruses and bacteria, but there is a certain yuck! factor in having saliva-and-snot-caked sleeves. The good doctor should have mentioned the obvious need to handle infected clothing carefully and wash it thoroughly...and promptly!

"Coughs and sneezes
Spread Diseases;
Trap them in your
Handkerchiev-es"

Public Information film from UK c. 1960.

"Coughs and sneezes
Spread Diseases;
Trap them in your
Handkerchiev-es"

brilliant!

"Coughs and sneezes
Spread Diseases;
Trap them in your
Handkerchiev-es"

The good doctor Oxford would probably appreciate a few extra lines of verse added to this clever poem. So I will add:

"But should you have no handkerchiev-es,
Trap them in your elbow sleev-ses."

Singing "Happy Birthday" twice while washing your hands in a public place is going to get you a reputation for sure!