The important clue here is the fact that you feel that the pain is like the pain that happens when you hit your "funny bone." This almost certainly narrows things down to some form of neuropathic pain, or pain related to injury
or inflammation in a nerve, because this is exactly the kind of pain that occurs when nerves are involved.
I think the fact that you work sitting at a desk all day is also an important clue. Desk jobs are commonly associated with repetitive strain injuries in the wrists and arms. Carpal tunnel syndrome
is the best example of this, but repetitive strain injuries can affect the entire arm as well. Essentially what happens here is that nerves in the wrist or arm become inflamed from the repetitive types of motion or pressure that occur when you sit at a desk, type on a keyboard, answer the phone, etc.
You should see your primary care doctor
about this as soon as possible, as they can confirm the diagnosis. They can also recommend treatment, which will probably involve taking some anti inflammatory medications and trying to figure out how to change the way you work (they way you sit, or the way you cradle the phone or type, for example) to minimize the strain.