Hmmm. Definitely there is stasis there, and the pulse indicates we need to move Blood externally to resolve the problem. Interesting that it is so severe a pain. GV 14 treats all the Yang channels of the limb, but also may become active in animals with chiropractic issues. If there isn't a prompt improvement you may want to seek out chiropractic treatment for the animal. In addition, I would be tempted to try St. John's Wort (Hypericum) for its reputation in dealing with both neuralgia and anxiety. Since it's summer, you may want to use the homeopathic form to avoid photosensitization reactions. If the dog is not outdoors for too long each day, the tincture is fine and we can supply that. Go with 0.2ml per 5 lbs BID.
The Kidney and GB points are interesting. Normally they don't become active in forelimb lameness - unless TB points are also active. But they suggest we should consider formulas like Xiao Chai Hu Tang. We add Qin Jiao to that to increase it's potency as an analgesic and anti-inflammatory.
As well, I guess the Kidney points make me think about Kidney deficiency with a secondary Wind invasion, leading me to consider formulas like Bu Gan Tang or even Chai Ge Jie Ji Tang. Truncal alopecia would respond to Bu Gan Tang, unless the animal has hairloss due to Damp Heat.
XFHMY is an option if the dog is quite Damp. Otherwise, if Damp is ruled out, I'd be tempted to try Bu Gan Tang and Hypericum. BGT would work here as an antispasmodic, synergistically working with Hypericum to relieve nerve root signalment. It's also an anxiolytic. Given what you've described, some pinching of the nerve roots between C3 and C7 sounds likely.
Good luck!
Steve