Is it normal to feel......well a impulsive urge to hurt

now as you have seen from the title this is quite a......disturbing topic so just bare with me till you hear the story. it started in my early teenage years. i would be sitting there quite happily painting or drawing and when i had finished i would get this feeling......like a surge of energy to just......destroy the painting i spent ages doing. it wasn't motivated be anger, it honestly just felt like i had to do it for pleasure. (not in that way) every time i made something i would get this feeling.....to just destroy everything i had made. this didnt worry me but at the point where it got to wanting to wreck other peoples i knew something was wrong. now onto the most......disturbing part. this /feeling/ developed into something more dark.....one day i was walking down the street and i saw this cat. then all of a sudden i got these horrible images in my head of me slaughtering the cat and combined with the feeling of /the surge/ i thought i was actually going to hurt the poor thing and be happy about it. thankfully this don't happen as often. but then.....the feeling started applying itself to fellow people. in my later teenage years i was passing a apartment block and i spotted a old woman struggling to get down the concrete stairs and once again i got the feeling to push her down them. i pictured myself standing on the top of the stairs laughing as she died.........every day i get these visions......this feeling......and im worried that one day i might actually carry out my urges.....im so scared....so very scared and combined with my previous post about not being able to feel empathy or sympathy i wouldn't even feel bad if i did......so the main question is.......am i a psychopath?