I suggest that anger at ourselves, and anger toward others are clearly two different activities, and should be handled differently.
Anger at ourselves is a form of self-rejection, a form of superego activity, a form of Inner Critic activity. We learn as children, with normal, healthy development that we must do, think, and feel within boundaries which are acceptable by our caretakers. We internalize their rejection of a myriad of impulses and inner experiences in order to "preempt" the painful and life threatening rejection of our caretakers. We do to ourselves --guide, censor, admonish, reject-- what we imagine they will do to us, on a feeling level.
This inner rejection is one of the ways that Inner Tension is caused in us. There is a war inside, which Dr. Sarno described as a conflict between the id and superego -between the "animal child" and the "inner parent."
Expressive writing and talking to experience and allow anger or other emotions can relieve this Inner Tension. We stop censoring ourselves. We allow feelings we think "aren't OK." We challenge the dominance of the superego for a short period, practicing freedom. This can be life-changing beyond the important factor in TMS work. This allows us to challenge the Goodist and Perfectionist personalities most TMSrs have.
So anger at ourselves needs to be met with a strong defense, not acting it out on ourselves. It can be very valuable to express anger at ourselves very mindfully to feel the power of this, to feel the hate or rage against ourselves. But the main practice here, in my opinion is to disengage this self-attack, you turn the anger back at the attacker.
One way is to see your inner child as being a victim, and you being the "mother bear" and defending, and this may go back to naming caregiving figures in childhood. The practice is to take the anger, the exact energetic anger which you feel directed at you by the superego, and express it outward, whether that is toward someone you feel criticized by, the superego, or parent figures. "I love being full of myself, so F-ck Off" might be a way you could respond to an attack that you were "to much."
In short when we're angry at ourselves, this calls for action to disrupt this anger.
Superego activity is a strong defense mechanism against all strong feelings.
It will also activate when you assert yourself with others.
The best book on this in my opinion is Soul Without Shame by Bryon Brown. Shows you how to deal.