> I need more sources to write a biographical criticism, which is
> explaining how Eliot's life influenced his poetry.

This might work for you:

    Colleen Lamos
    "Deviant Modernism: Sexual and Textual Errancy
    in T.S. Eliot, James Joyce, and Marcel Proust,"
    Cambridge University Press,
    ISBN 0-521-62418-5

A quote:

    The displacement of matricidal fantasies onto a murderous mother is
    the compulsively enacted scenario of Eliot's early poetry. A cursory
    review of his poems from "Prufrock" through "The Waste Land" produces
    an inventory of fatal Cleopatras, poisonous Belladonnas, sadistic
    salon matrons, and rapacious whores.  Correspondingly, these texts are
    littered with the corpses of young men, many of whom have drowned in a
    lethal, uterine element.

See more at:

   Rick Parker

P.S. I think it is a shame that Miller's book is out of print but it
is and it must be sought out at libraries or second hand book stores.
These are some on-line used book stores (actually, they are not stores
themselves, but have the inventory databases of hundreds of used book
stores which actually ship the books):