The zombie that scares you, indicates the things you dont know and things that threatens you. The zombie is also a symbol of something that is no longer alive. If you see the zombie that is chasing you, you are dealing with your negative past. The other explanation says that you are still not feeling safe from the horrible things that happened in the past.
Dream dictionary: Zombie dream meanings
If you are a zombie in your dream marks that you are rejected from the environment. You feel humiliated emotionally and physically because nobody pays any attention to you. Perhaps you are feeling that your inner world is dying. You just live and act without any satisfaction, you just like a zombie without any feelings.
Dreaming that you are a zombie indicates that you are physically and/or emotionally detached from people and situations around you. You feel out of place. It may also indicate that you feel discouraged and unhappy.
If you dream of being yourself a zombie, it means that you have no idea what is going on around you. You must pull yourself together, otherwise you wont be able to live in this society.