Is "I saw a dog. A dog was barking loudly" correct?

Why

Rohit's assumption that the same article should stick with the same noun throughout a story feels tidy and consistent, but "a"/"an" and "the" are actually doing two DIFFERENT jobs depending on whether the listener already knows which exact one you mean. "A dog" the first time introduces a dog the reader hasn't heard about yet — any dog, not yet identified. Once it's been mentioned, though, both speaker and listener now know exactly WHICH dog is being talked about, and English switches to "the" to mark that shared, specific knowledge — "the dog was barking" means that particular dog just introduced, not some new, unrelated one. Repeating "a dog" the second time would confusingly suggest a completely different, second dog had just shown up. Test: notice how a story naturally flows this way — "I met a boy. The boy told me a story. The story was funny." — each new thing gets "a" on first mention, then switches to "the" once it's known. His teacher is right: "the dog" is needed on the second mention, since by then both speaker and listener know exactly which dog is meant.