With a spider bite there is usually swelling...much like a snake bite. Next there is skin evidence because the tissue that received the venom dies. If the leg appears normal, it was not a spider bite.
Unfortunately you are correct to see a neurologist as quickly as possible. It is progressive, and an neurologist is the best option to not only diagnosing the problem but treatment and prognositc help as well. There are many things that can cause the signs you describe...it sounds like what we call Upper Motor Neuron signs which can come from the spinal cord itself of the brain. I do hope things are resolved quickly.
Let me know if you have further questions.
Dr.V
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Dr. D.A. Vamvakias
Veterinarian