Normal or abnormal thoughts?

Ever since I became pregnant with my second child I have become worried about something happening to me, my husband, or my children. It’s not constantly there or overwhelming to the point I can’t function, but it’s there. Things like, what if I trip and fall down the stairs with the baby, what if I get in an accident, or other things that people could or may do to my children. I’m not having any suicidal or homicidal thoughts or having trouble sleeping or functioning.

Is this normal? Is anyone else experiencing this?