Beat cream and 3 tablespoons sugar together in a bowl using an electric mixer until stiff peaks form. Refrigerate until ready to use.
Beat ricotta cheese, sour cream, and sugar together in a bowl. Fold in the whipped cream gently; add rum.
Pour coffee into a bowl. Dip the ends of half of the ladyfingers in the coffee. Arrange ladyfingers dipped side-down into a single layer in a 2- to 2 1/2-inch deep rectangular serving dish. Spread half of the ricotta-cream mixture on top. Repeat dipping and arranging the remaining half of the ladyfingers; spread the remaining ricotta-cream mixture on top. Cover with plastic wrap; refrigerate until fully chilled, 10 to 12 hours.