Even if appendicitis was cured through IV antibiotics, appendectomy should be performed regardless because gettting appendicitis once increases the chance of getting it again a lot, and appendectomy is a decently well-understood and very safe surgery that has almost no side effects.
The doctor...
Is no one going to comment on the art style changes? The earlier art style was better than what it's like now, because all the characters looks so much more... childish I guess?
Like viliml said, he was wearing the ring while he was wearing a long sleeve and she had long hair, she currently has short hair, so the him with the short sleeve is the more recent one.