Does the divorce that I uttered in a state of intense anger, in which I was the cause of that anger, count, knowing that this is the first time I have uttered the word of divorce, and my wife was menstruating, along with my desire for no one to know about this?

As long as you pronounced a clear divorce, being conscious and not overwhelmed in your intellect, your divorce has taken effect, even if it was during a state of intense anger. This is because an angry person is held accountable for what they utter as long as their intellect remains intact. The validity of the divorce is not hindered by the wife being in her menstrual period, as the divorce of a menstruating woman is valid according to most scholars, and this is the fatwa (definition) we adhere to.

Since this is the first divorce, you may take back your wife during her 'iddah (definition) (waiting period) without needing to refer the matter to a judge. It is sufficient for you to say: "I have taken back my wife." It is preferable to have two men witness this reclamation.