Is it normal to lack guilt?

I've hurt people in the past and I've even had immensely violent/graphic thoughts about slowly torturing/killing people and making them suffer as much as humanly possible. I've gotten into fights in elementary school and caused some other students and even teachers to get stitches. I've hurt family members. Despite all of these things... I've never felt guilty about any of it. I honestly feel like I was born to fight and kill. I've only felt guilt when it comes to my girlfriend. I'm terrified of hurting her and any time I feel like I've hurt her, I feel like I'm having severe chest pains and I apologize profusely and breakdown emotionally. She's also the only person who's been able to calm me down regardless of any situation, including a couple times where I was almost completely consumed with anger, rage, and hatred (none towards her, I've never felt angry or hatred towards her).

Is this normal? And please... keep your troll answers to yourself.

Note: I've NEVER acted on my "soulless" thoughts. The times I've hurt others was when I was blinded by anger or by accident. I know right from wrong and don't intend on hurting people on purpose and for no reason. I'm a pretty tame person when it comes to violence.