Which Punctuation Mark Should Be Used To Show Repetition?

Is it okay to use an em-dash if I want to show repetition of word/words or phrase in a sentence?

I told you ― I told you to put on a different voice.

It depends on how this is being spoken. (Note that I am an American English speaker.)

Chicago Manual of Style (13th ed) has a Paragraph 5.12, entitled "Faltering Speech."

Ellipsis points seem to suggest faltering or fragmented speech accompanied by confusion, insecurity, distress, or uncertainty.... The dash, on the other hand, suggests some decisiveness and and should be used for interruptions, abrupt changes in thought, or impatient fractures of grammar without the confusion or indecisiveness suggested by ellipses.

Your example seems to be an "impatient fractures of grammar without the confusion," so the dash is appropriate.

I told you ― I told you to put on your shoes!

However, if the voice were pleading or plaintive, it might be better rendered:

I begged you... I begged you to put on a different dress.

In the case of repetition, especially for emphasis, the comma is king. Consider the hymn "How firm a foundation" by John Rippon (1787):

That soul, though all hell should endeavor to shake / I’ll never, no never, no never forsake.

(Source)

And there's Winston Churchill's famous speech (1941) which repeats many nevers for emphasis:

... never give in, never give in, never, never, never, never — in nothing, great or small, large or petty...

(Source (corrected for punctuation))

So for very short repetitions, the comma works fine.

I've always, always, always reminded you to put on a different voice.