I have things that push me past my limit and I can be pretty biting, and it takes a lot of pushing for me to just totally lose it. I regret it after, but I'm okay with being human. Took me a long time to be okay with myself, I was usually much more forgiving of others or made excuses for them, now I work on forgiving myself and recognizing my default is pretty darn good, and for the rest, there is usually good reason. I like the Stoic idea of just doing my best, and when I haven't, learning from it and working to do better. So many people can't or won't look deeply at themselves and strive to improve, or at least not without accompanying self-flagellation or self-condemnation, and that doesn't do anyone any good. If I've done something I don't respect myself for, I resolve to learn and not do it again if I can help it. It's important to me to respect myself and be worthy of my own respect and compassion; I've learned that I can then expect them from others, and if they don't respect me or forgive my honest mistakes, they're not someone for me to be around or I'll end up back in the place of biting or losing it.
I respect that you have self-awareness. The angry part of you has reasons for acting that way and deserves respect, love, and understanding, too.