If your mother and you are constantly fighting to the point where it is physical most of the time and you have a job and another place to stay would it be possible for you to move out?

If Mom has custody and you are under the age of majority (18 in most state, in some it's higher, but it's never lower) then you cannot leave home without her permission unless you have been emancipated. If there is abuse, then you need to report it to the authorities! If you are in a dangerous situation then they will remove you from the house and place you under state care.