Longstanding Yin deficiency commonly exacerbates any latent Shao Yang disharmony, leading to Yang rising tendencies that can produce the restlessness and agitation of canine cognitive dysfunction as well as things like head tremors. Dysbiosis in response to antibiotic use is also a common Shao Yang complaint.
If Shao Yang disharmony continues, with Yang not able to fully integrate into meager Yin reserves, Source Qi declines, reducing stamina and producing the pale tongue. Qi deficiency itself creates agitation as the patient gives voice to their discomfiture at their loss of confidence and the ease with which they are overwhelmed.
In summary, then, we likely have three intersecting concerns: Yin deficiency (potentially causing neck tightness and spasm that creates forelimb lameness, especially with extended use); Shao Yang disharmony; and Source Qi deficiency. Each can be a cause of one of the others, so rather than trying to 'treat the roots' by working out their sequence in this dog, let's focus on treating 'branches'. In other words, treat the layer that presents itself, then wait for the pulse, tongue and symptoms to shift, exposing the next layer of concern. Only once all key layers are addressed will symptoms subside on an enduring basis.
Normally, my temptation is to start with Shao Yang and Yin deficiency, but given the pale tongue and weak (Qi) pulse, I would suggest something basic like Liu Jun Zi Tang first. See if restoration of Qi helps quell his agitation. If you like, you can target the psyche a bit more specifically, by using Tian Wang Bu Xin Dan. Eventually, though, I can see that complete resolution might require use of a Shao Yang formula. The pulse should become stronger with the use of tonics, eventually signaling the need for Minor Bupleurum or one of its derivatives.
Regarding current therapy, if Yang is rising, then it will do so even more (thus aggravating the dog) with Body Sore and any other Wind expelling formula. These formulas contain aromatics, which drive Yang energy upwards and outwards. They would be contraindicated in a Yang rising case, or a case where Yang is trapped in the exterior layers.
Regarding the forelimb lameness and response to chiropractic, that signals a neck issue. Rather than using Body Sore to address it, consider Bu Gan Tang instead. It is a muscle relaxant and Blood and Yin tonic, but will astringe rather than expel, helping to draw Yang inwards and downwards rather than pushing it outwards. In other words, it should help the dog as a whole, and not just the neck. If you use it, then probably just Liu Jun Zi Tang is fine to use in tandem with it to address the Qi deficiency.
Regarding pain relievers, if the dog is prone to dryness, NSAIDs will aggravate that tendency, risking GI ulceration. Normally I would recommend Yi Guan Jian as a treatment, but if the morning vomiting signaling Stomach Yin deficiency has subsided, then focus your Yin and Blood tonifying efforts on the musculature, Kidneys, and Heart instead, using Bu Gan Tang. The response to chiropractic suggests the forelimb issue is arising from nerve impingement, so trying something like gabapentin instead of the NSAID may be more useful and better tolerated. St. John's Wort alleviates both anxiety and nerve root impingement and is a consideration here as well.
Hopefully all these ideas are helpful and the assessment accurate. Let us know how it goes!