I just realized my girlfriend is a sociopath
What makes you think your girlfriend is a sociopath?
She's really cold at times. And she also acts impulsively.
I think it's good that you've come to the realization that your girlfriend is a sociopath so you can decide what to do. You should think about whether or not you want to stay with her.
That's true, I also feel like she has never cared about anyone but her self.
So do you have any idea what you want to do now? There are options like breaking up or asking her to see a therapist.