Nellie is usually given as a diminutive form of Nell, itself derived from Eleanor, Ellen or Helen. (I named my daughter Nell, as a variant on the family's use of Eleanor in a number of names.)
According to 'Behind the Name', Nell is a "Medieval diminutive of ELEANOR, ELLEN (1) or HELEN. It may have arisen from the medieval affectionate phrase mine El, which was later reinterpreted as my Nel.
VARIANTS: Elea, Ella, Ellie, Elly, Lenore, Elle, Leanora, Lenora, Nelle, Nora, Norah
DIMINUTIVES: Nellie, Nelly"