If you can't get a diagnosis that indicates to me that you've seen a Neurologist? You're asking if white spots on your cerebellum could cause your symptoms, does that mean you have had a MRI of the brain?
If you have seen a Neurologist, what is he/she stating their next plan of action to help you toward a diagnosis? Did you have a MRI of your cervical and thoracic spine as well? What about other testing? For example: evoked potentials, blood work or lumbar puncture? What has been tested and what came out normal?
Apparently your symptoms are not normal and there's something going on. As to what it is, we here can't diagnose but may suggest how you can better be an advocate for your health.
Our forum has a great Health page here:
http://www.medhelp.org/health_pages/list?cid=36
There's a few pages to scroll through but it is worth it because the subjects are richly explained in terms a non medical person can understand.
Let us know.
PS - Welcome to the forums!
Lisa