the baytril is the big gun antibiotic and the prednisolone is a steroid and is the anti-inflammatory. I think the vet is right to think neurological
but a blood panel is first step and when doing blood panel do the bile acids to rule out liver disease. I really do not think teeth would cause this as my boy had 10 baby teeth removed and never acted like that he was like a little shark but he was only 6 months how about yours?