There are a few websites out there that get into some common dream scenarios, Dream Moods I think is one of them. Being chased in a dream is usually not enjoyable, but many times it's just our subconscious telling us that there is an issue in life we feel out of control of.

The people chasing after you, their description, and general demeanor, could be a clue about what issue your subconscious wants you to work on. Since it seems that for you, the characters in your dream had some relationship or interaction with your family members (mother, brother), that might be a good area to start examining. Good luck!