This sounds like vestibular disease. It can be due to an inner ear issue or a neurlogical one.
You can read about this problem here
http://marvistavet.net/html/body_vestibular_disease.html
It might be due to a neck issue so you can see if swapping to a harness for walks will help.
You might also want to check with a veterinary neurologist if you think its not from inner ear issues.
Hope this helps you!
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