To find sheet music for these songs, and others, go to the search page of The Lester S. Levy Collection of Sheet Music and set the date range to the year(s) you want. Of course, that means you will be finding songs according to the copyright date, not necessarily the year in which the most copies were sold, so you might want to go back a year or two earlier.

It brings up 117 songs for 1921 alone. Of course, most of those were quite obscure.

Here are a few more to look up:

1921
"I'm Just Wild About Harry" (Eubie Blake)
"April Showers" (Louis Silvers) Al Jolson sang it ex show Bombo
"I'll See You in My Dreams"
"There'll Be Some Changes Made" (W. Benton Overstreet & W. Higgins)

1922
"Chicago" (Fred Fisher)
"Way Down Younder in New Orleans" (Creamer/Layton)
"My Buddy" (Walter Donaldson)
"Carolina In The Morning"