I sang this growing up and I was looking for the words, but none of these fit exactly what I remember singing.
I think the closest went this way...

Miss lucy had a baby
his name was tiny tim
she put him in the bath tub
to see if he could swim
he drank up all the water
he ate up all the soap
he tried to eat the bathtub but it wouldn't go down his throat

Miss lucy called the doctor
the doctor called the nurse
the nurse called the lady with the alligator purse

Mumps! said the doctor
Measles! said the nurse
Nothing! said the lady with the alligator purse

Shots! said the doctor
Medicine! said the nurse
Pizza! said the lady with the alligator purse

Miss lucy punched the doctor
Miss lucy kicked the nurse
Miss lucy payed the lady with the alligator purse.

(we didn't sing the in and "out" verses, but that was probably because we used it as a clapping game and not a jump rope game.

The voodoo/medicine woman seems most likely -- but I have no true idea.