Since you are a Zombie movie fan, there is no surprise that you would dream of it. However, that may become some symbol in your life. In your case...
Zombies = fear, uncontrollable.
You may be having some fear about things you cannot control Projecting yourself going to a safe place to escape from them shows emotionally you are feeling insecure. Even though in your dream, they don't catch your or kill you. This symbolizes some fear subsides in your subconscious mind. This may mean that there is something you are feeling helpless. In other words, you are trying to show your capabilities to things you can do, but you just don't have chance to do it. By the time, you have such chance, very often you will get blamed for the mistake you made or not getting credit you should deserve. You are feeling insecure therefore and you want to vent out your feeling and basically you are trying to show your support to people and be appreciated in some aspects of your life.
Having recurring dreams show subconsciously you are still feeling left out in some sense.