Question: What is the literary device used in “She’s not just showing you what *she made*. She’s showing you what *she’s made of*”

At first, I thought it was chiasmus, but it does not really fit.
Certain that it is a type of repetition, but I do not know what it would be specifically called.

Answer: 
Examples of the rhetorical figures of speech called zeugma or syllepsis are relatively easy to spot but more difficult to analyze. Even the definitions of these two figures can be difficult to understand!

Nevertheless, syllepsis and zeugma can be effective and even memorable ways of phrasing words and are worthwhile studying for that reason. An example of syllepsis which parallels your example is the following:

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> He lost his coat and his temper. 
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Notice the double sense in which the word *lost* is used. Someone can *lose* a possession, such as a coat, by leaving it somewhere absentmindedly, only to return to the place where it was left to find it gone. 

By the same token, a temper is something which all people possess, and most of us keep it in check. When it breaks free from its self-imposed captivity, however, we say it was lost, as in 

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> "He lost his temper when his car stalled in the middle of traffic." 
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> 
> 

Your example takes the verb *made* and uses it in two different senses. The first sense brings to mind, for example, the making of a piece of art, such as a painting or a sculpture. The second sense brings to mind the stuff which a person's character is *made* of--the stuff which comprises a person's character. 

That "stuff" could be anything from a creative, inventive spirit, which results in a work of art being *made*, to an angry, invective attitude which results in a real mess being *made*, thus showing people what we're made of (and it's *not* pretty!). 

Syllepsis enables the speaker or writer to use fewer words in expressing a thought, but it also requires the reader or listener to "pick up on" the two (or possibly more) senses in which a particular word or phrase is used.
We did this in our English lesson yesterday so I'm pretty sure this is right.

I believe the term you're looking for is '**anaphora**'.

It's basically when you have sentences that are comprised of the same words/phrases (which I think is the case here).