The phrase "visibly irritated" is correct and usable in written English.
You can use it to describe a person or situation in which someone's anger or agitation is clear and noticeable. For example, "My boss was visibly irritated when I arrived late to the meeting."
"Not while I'm speaking," a visibly irritated Obama snapped back.
MIA is visibly irritated, shaking her head and leaving the stage to switch microphones.
She became visibly irritated, however, when about 20 students tried to disrupt her speech.
When asked why Cuba still held political prisoners, a visibly irritated Castro responded by asking: "What political prisoners?
This declaration -- categorical, a little edgy, a little holier-than-thou -- visibly irritated several of the people around the table.
When challenged, he can become the Mitt Romney that aides don't want anyone to see — visibly irritated, annoyed at being questioned.
But a visibly irritated European Commission says the time has run out for the Polish government to privatise and restructure the two remaining state-owned yards.
And the visibly irritated mayor told reporters he would not heed fiscal advice from state and federal lawmakers — or from the city's economically struggling news media.
But he was visibly irritated when asked whether his diplomatic blitz was merely designed to buy time with his Western interlocutors.
That essentially was the question that visibly irritated members of the Waterfront Commission of New York Harbor asked at a hearing in Lower Manhattan on Tuesday morning.
In an Oval Office appearance, a visibly irritated President Obama showed reporters a nearly empty supply cabinet and said, "They have manufactured this crisis," noting that he will be out of paper clips and Post-its by August.
