"zdenerwowany" could work, zirytowany/poirytowany/podirytowany would be closer, also "wkurzony" seems very common, but that's colloquial. "wkaczony" would be the version you will find in Donald Duck comics ;)
If 'annoyed' was accepted, then I guess 'irritated' should be as well. Added now.
A 'more better' version would be 'zirytowany', 'podirytowany' (the latter is kinda like 'a bit irritated').