I want to say, "Ergo, something comes from nothing and nothing comes from nothing." Is it correct to translate this as: "Ergo, ex nihilo aliquid et ex nihilo nihil fit"? I'm aware that "ex nihilo aliquid" means "something out of nothing" and that "ex nihilo nihil fit" means "nothing out of nothing".
Your translation is correct and proper.
Your translation is fine, but a Roman may have preferred to express the shared prepositional phrase only once, perhaps like this:
Ex nihilo igitur fiunt et aliquid et nihil.