Is it normal to sometimes feel no emotion?

well, i'm not sure if this is normal or not, but its started for a while now. Sometimes I feel over the amount of emotion and can get realy sad and really happy so easily like if someone spelt my name wrong i'd get really upset. While other times i have no feeling, at all. Like i could kill a baby or a person and not feel quilty, sad or regret. I could watch someone in pain and not feel sorry for them as if they deserved it, I could drown a puppy (not that i would) but if i did I woultn't feel sorry for it.. but only occasionaly, if i thought of that when i felt feelings i would never ever be able to do something like that.. I cant control it, its as if all my feelings just leave my body.. whats wrong with me? should i tell my mum? or see a counciller.. or am i normal?