A good question to ask yourself when annoyed is this: Why am I annoyed?
And check this answer you receive against Scripture to find out if this is a sinful reason to be annoyed, or a godly reason.
For me, I was annoyed at the Capitol riots because it seemed that Christianity was being misrepresented, as there were those claiming the name of Christ at the riots. This saddened me to read about, as this is one of the devil's tools to lie about the Gospel and drive people away from the truth. I felt that it was important to strengthen my own witness to counteract this, and that helped me feel better.
So if it is a sinful reason to be annoyed, recognize it and its emotional harm and understand biblical truth to replace it; if it is a good reason, then taking action based on that good reason can help.