What type of doctor should I visit for arm numbness most likely the result of repetitive motion at work?
Your PCP. While i can't be certain, the most likely cause of numbness in your situation is that one of the nerves in your wrist, arm or neck is being irritated or pinched. This is something that your primary care provider, or pcp, can help sort out and possibly treat effectively, and refer if needed. Pcp's usually include family practice or internal medicine doctors, and nurse practioners.
PCP First. See your pcp first. If there is a simple problem, they can treat you and avoid unnecessary testing and treatment. If a referral is needed, then they can make it. If you are unwilling to do this, then see a neurologist or orthopedist (preferably a hand surgeon). Just my opinion.