If I give in to him, I will be annoyed with myself.
He was very annoyed about the whole affair.
I'm aware of the meanings of them and I'd just like to make sure my understanding about the usage is correct.
The phrase "annoyed about" is usually followed by something while "annoyed with" is for someone.
Is my understanding correct?
Besides, are there any other adjectives which work this way, like "disappointed", "excited", "upset"?
Yes, you are correct that "annoy" plus "with" usually requires a person as the complement of "with" whereas "annoy" plus "about" usually requires a situation as the complement of " about."
I cannot recollect at the moment a difference that is precisely similar to this one, but frequently a difference in prepositions involves a difference in meaning. Here is a different but perhaps similar example
"make a big difference to your English" vs. "make a big difference in your English"
Unfortunately, the effect in English of different prepositions on meaning cannot be reduced to any consistent rule that I have ever been able to articulate. It is one of the most extreme obscurities of the English language. As a native speaker, I have been doing it for decades but still cannot fully explain it.
