The numbness and coldness do not sound like torn nerves. that would irtractable hyper pain signals. It seems more like a CRPSor hyper signals, and or slow signals. THere are some test that dr. Scott Fried does that can perhaps shed light on what is going on.

For the short term, I would see the pCP for a shot of TOradol and at least get the inflammation helped. Not the pills, you need the good ol shot. When my dd was real bad to avoid an ER trip I would get her to PCP for the shot.
I would consider too a blood clot for that much pain? Is you arm itself swollen?
There are sheathed and unsheathed nerves that carry signals to the brain. It sounds like the signals are traveling the super hwy to the brain. The others is the cold signals. So both types of nerves area reacting.

If nerves worn torn, I think that it would be a problem making the muscles move because the brain signals would not be making it.
But, with a stretch or overuse assault, the whacky signals go on .
Is it weather related this week? THe storm systems and rain have me holding my arm and hand in a lot of pain I was at first relating to all the photos, diagrams and computer entry for the escalation in claims this week. I drove myself today and stood in the rain for two claims and tonight wraped my arm in heating pad and the side of my neck by head in ice.
Took Bayer, a valium and went in my room to sob. My left wing from holding my arm up is just feeling like a horse kicked it. My lumbar is the same. So i thought the rain and pressure system really affected more so this week.

Can you get some appointments set up to rule things in and or out?