I have a dull pain in my right wrist, just about where the bone of the arm connects on the outside.

Need more histroy : If there is no history obvious injury than it can be carpal tunnel syndrome, or tendon inflammation like dequervain's tenosynovitis, presenting as wrist pain.

Busy anatomic area !: There are multiple possible causes in this area, but tendonitis and arthritis are both high on the list. You can try a resting wrist splint from the drug store and over the counter medications such as Acetaminophen or Ibuprofen if needed. If no relief, see your doctor.