I can definitely relate to what you've described. I've had a problem with rage since I was a child. It's very rare that anyone actually witnesses it when I go into a rage. And I will say that I have never, under any circumstances, lost it with a child or animal. I have, however, broken many items in my life, oftentimes an item that I really regret breaking after it happened. Once I became so angry that I set something on fire (a lampshade - scared the hell out of me).
I cannot even begin to diagnose you, but I can tell you that I've been diagnosed with bipolar disorder (the rages almost always come along with mania...but certainly not every time). I have definitely asked if I have BPD and have been told that I do not. I did grow up in a home in which there was a tremendous amount of anger, rage, fury, and violence. More than anything I think that made an imprint on me...when I feel angry I can actually envision damage done in my childhood home and that often happens just before I break something.

I became very serious about stopping my raging when I was arrested for domestic violence and spent the worst, most terrifying night of my life in jail. I just plain stopped allowing myself to have rage outbursts by counting to 10, by walking away, by recognizing when my level of anger was quickly escalating and forcing myself to stop and breath - sitting in a chair with my feet flat on the floor while I breathe deeply and evenly definitely helps interrupt the rage flare-up. So does drinking water, which distracts me log enough to intervene with the rage. But I was already in the mental healthcare system so it was easier to get control of myself...I was on the meds; I was learning the tools.
Mood stabilizers are extremely effective in keeping anger from escalating into rage.

One thing I want to mention. Please, please don't scold your cat or become angry with it for any reason. Cats poop on the floor for very clear reasons. They are, by nature, extremely clean animals. If a cat poops on the floor it is ill, it's box isn't clean, or it is very stressed. No cat makes the connection between being scolded and the poop on the floor. In addition, their hearing is very, very sensitive...being scolded only causes a cat to feel extremely upset and stressed.

My suggestion to you is that you get professional help NOW. I mean it. Take it from one who has done some serious damage to her life because of rage outbursts: One of these days, you will end up in deep trouble and you won't be able to go back. I'm really glad you've opened up about your serious problem. Now it's time to take action and make sure your raging outbursts do not continue.
Best to you.