Is ""Now look what you did," I griped. "There went our breakfast. Can't you two wait till I set the eggs down before you go shovin' me all over the country?"
a metaphor?

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Personal Note -->

This quote is noticeably from The Outsiders, which I personally know as a great book!

But anyways, this is the exact quote:

"Cant you two wait till I set the eggs down before you go shovin' me all over the country?"

Which figurative language device is being use here?

This is a hyperbole, as the meaning of the quote is obvious but it is simultaneously exaggerated at the end of the sentence. A metaphor is different, basically being a simile without the 'like' or 'as' next to it.