Serial killers generally have no remorse for their actions or their thoughts. You've clearly shown some emotional disturbance from the way she reacted.
I get those thoughts too, sometimes. And actually, it can for a form of OCD. I obsess over random things and thoughts, sometimes not the most pleasant of.
Now, do I get random thoughts of hurting someone? Yes.
Honestly I do, but I know that I would never act upon these thoughts, nor do I really want to. It's more of a simple "if I push her into the street, what would happen?". Something of course, I wouldn't want to do. But the thought, as long as it's just a thought, isn't anything to be worried about as long as they're not constant and as long as you know to not act upon them. If that makes any sense.