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Hello. I'm sorry to hear about your dog.
This is not just arthritis. Arthritis can cause weakness and difficulty walking, but not paralysis. Paralysis is due to something pressing on the spinal cord or affecting the blood supply to the spinal cord. This could be a spinal tumor, disc herniation, stroke to the spinal cord (called FCE- fibrocartilagenous embolism) or meningitis.
The only way to know for sure, is to get a CT or MRI of the back. That is the only way we can see the spinal cord and discs. If it's something compressive (disc or tumor), then surgery could be curative. If it's inflammatory or a stroke, then continued physical therapy and supportive care can be done. If a metastatic tumor, there may not be anything that can be done. It just depends on what is found.
I would try to get in touch with a veterinary neurologist in the area to get a second opinion and then decide if imaging is the way to go.
I hope this helps, let me know if you have any other questions.