Nightmares involving fighting another can have many meanings. You could have symbolically divided yourself into parts which then fight it out. Or when someone attacks you with words or thoughts in waking life, you might translate this into a dream where you are being shot at with a gun. If your feelings are really hurt, in the dream the bullets might hit your body. If your feelings are unhurt in the dream, the bullets probably missed you.
Fighting generally symbolizes conflict.
The location of the fight is important. For example, if it is at your place of employment, the conflict is there. You could have strongly conflicting emotions about your job. A good response to such a dream would be to try to consciously understand this conflict. By understanding it, hopefully, you will be able to stop this fight within yourself.