Here's a longer version of the poem posted by Nathan in Texas (though it is probably not the song OP wanted). Note that this version has no author attribution.

From Routledge's Readings: Comic edited by Edmund Routledge (London: George Routledge and Sons, 1871), page 79:


THE TWINS.

In form and feature, face and limb,
    I grew so like my brother,
That folks got taking me for him,
    And each for one another.
It puzzled all our kith and kin,
    It reached an awful pitch,
For one of us was born a twin
    Yet not a soul knew "which."

When quite a little infant child
    My trouble did begin,
For when I called for nourishment
    'Twas given to the other twin;
They gave "me" Godfrey's cordial
    When he kicked up a shine,
And when his nose was troublesome
    They took to wiping mine.

One day to make the matter worse,
    Before our names were fixed,
As we were being washed by nurse
    We got "completely mixed;"
And thus you see by fate-decree,
    Or rather nurse's whim;
My brother John got christened "me,"
    And I got christened "him."

This fatal likeness even dogged
    My footsteps when at school,
For I was always being flogged
    'Cause he turned out a fool.
But once I had a sweet revenge,
    For something made me ill;
The doctor came and gave poor Jack
    A black draught and a pill.

We both set up at last in trade,
    My prospects were but grim;
The people bought my things, but paid
    The money all to him.
And once when he had had a drop,
    And broke a P'liceman's nob;
They took me into custody,
    And fined me forty bob.

This fatal likeness turned the tide
    Of my domestic life,
For somehow my intended bride
    Became my brother's wife.
Year after year, and still the same
    Absurd mistakes went on;
And when I died the neighbours came
    And buried brother John.