Few people are really symmetric mate, so first of all don't start to worry that you are a freak!
I wouldn't really advocate starting to train your arms seperately, try if you can to use the same weight and reps.
Have you ever damaged that arm or shoulder?
You may have a physical issue with a nipped nerve, basically reducing the nervous stimulation of growth which comes from your cns. A physio would be able to help you ascertain if this is the case and help treat it.