Leaving Gee's Bend by Irene Latham

Ludelphia Bennett has never been outside Gee's Bend, Alabama, though she's ten years old. But when her mother becomes deathly ill, Ludelphia risks taking the ferry raft across the Alabama River to find a doctor--even though her family has no money to pay him. The flood-swollen river pulls the ferry loose, and Ludelphia, who never learned to swim, is swept far downstream. All her determination is needed to get safely to town and overcome both the river and an enemy she didn't even know she had.