The process of self-inquiry is useful when you want to deepen your understanding about yourself and/or your life. Asking a question, posing a question and then just allowing it to be in the back of your mind, can bring about an insight, a new idea, an awareness that wasn't there before. One way of doing this, is to keep a journal. Write your questions in it and then go about your day. Upon re-reading your journal you may observe that you have had answers revealed to you about your questions.
When an irritation arises in your life, developing an attitude of "allowing" can be very helpful. There may be something deeper the irritation is wanting to bring your attention to.