It’s just possible that you are really one of the lucky people who has never done anything to be ashamed of. It does happen.
And anger at bullies rather than embarrassment is a healthy response indeed. It’s the bullies who should be feeling shame.
It may be that your experience as a victim when you were young taught you that anger was a more helpful response than embarrassment. You therefore learned to transform all embarrassed feelings to anger. That’s only an educated guess. I’d need to know more about you to say more.
Since you describe yourself as fully able to experience the full range of other emotions, I’m not worried about you. However, I do think it would be helpful for you to expand your response repertoire to include embarrassment when it is appropriate. A psychiatrist isn’t likely to help you with that these days since their jobs usually require them to limit their sessions to a very short time and to focus on pharmacology. I suggest you instead contact a local licensed psychologist, social worker or mental health counselor to talk it over. They will have the ability to hear your entire story instead of only the 200+ words of your letter.
I wish you well.