= 追い打ちをかける。
(idiomatic) To further a loss with mockery or indignity; to worsen an unfavourable situation.
今までずっと"add salt to injury"だと思っていた。というか、
(idiomatic) To make an injury, physical or emotional, feel worse.
これと混同していた。なので気になって違いを調べたら、
Basically, "add insult to injury" is just a general statement. On the other hand, "rub it in" is a specific action done by someone. Usually, you wouldn't say a specific *person* "added insult to injury" - it just refers to when a bad situation gets even worse due to something.
But "rub it in" is *always* done by a person.