I could not find a specific name for a fear of harming others. There is an entire list of phobias and I did not even get through the As! Everything I found on the subject says that fear of harming others is a symptom of OCD or related to bipolar disorder.

I would say this is definitely a symptom of Obsessive Compulsive Disorder, or OCD. I have OCD and I go through the same thing every day. Fear of accidentally or intentionally hurting animals or people. Even though I know that I would never do this intentionally, I have the fear. It is part of having OCD. If you search "fear of harming others" and try to find a discussion board or forum about it, you will see that many other people have the same fears as you. Don't worry, you're not crazy. Hope this helps.

This symptom, while probably irritating to you isn't dangerous. It's good to worry about the safety of others. However it does sound like classic OCD and the disorder can get out of control very quickly if untreated. I'd suggest you talk to a psychologist about what you're experiencing.