When I was younger, I often had the same dream over and over and I never knew what it meant... from what I can recall now (over 30 years later), I would be moving along a single thread or wire and there are faces in the dark surrounding me. If the faces weren't agitated, the line I traveled on was smooth and calm, but if the faces became angry, I felt the anger in my dream and the line or wire I traveled on became like a seismograph, all erratic and crazy until the anger subsided and the faces were no longer agitated and the line I traveled on became smooth again. I haven't had this dream in years and actually want to so I can try and understand what's going on within. There was also another dream that I kept having... one of the Super Mario Bros was standing outside in our backyard, giant hammer in hand with rain and lightning, trying to come through our sliding glass door as I hid under the kitchen table. This could have just been my childish mind playing tricks on me, but it did scare me.
It seems like the line represented your life, and you were worried about what would happen if other people got angry at you, or if you couldn't control your anger, and how that would effec your life. Since you felt the anger in your dream, you could have been repressing a lot of anger about something and the dream was a warning that you had to keep that anger in. Dreams about being chased are common in children. They often have to do with not being able to avoid situations over which they have no control - children don't have much control over their lives compared to adults.