And just to put a final touch on things:
For the verse, add one more A7 --
C, E7, A7
F, A7, Dm-A7-Dm. The last three chords are for "I didn't care", one for each word.
This is a great song that used to be warbled and embellished by many benighted singers in the '60s. It wasn't until I heard the Bessie Smith original, where she sings it absolutely straight-ahead, often holding one note while those ragtime chords change underneath, that I fell in love with the tune.