The dizziness with the neck movements and occasional numbness in right arm can be because of the cervical spine disease. If you have any history of neck injury or whiplash, this is further substantiated. The numbness is explained on the basis of pinched nerves in the neck because of the herniated disc in the cervical spine and so do the dizziness which is called as cervicogenic dizziness or cervical vertigo. Still, the investigations like MRI are needed to establish the diagnosis and ear causes should be ruled out for the dizziness. Read here on this link;
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A dizziness of this magnitude will need thorough evaluation. A dizziness associated with benign paroxysmal positional vertigo (BPPV) is profound in morning time. Out internal ear is responsible for the balance and is connected to the brain. Any dizziness will need certain tests by an ENT specialist to assess its function and role in the dizziness. The roller coaster rides sometimes can give jerks to cervical spine and a cervicogenic vertigo can be precipitated. But in your case, internal ear inflammation, BPPV, meniere's disease etc should be first ruled out or ruled in for the dizziness. Read the causes and other details of the dizziness;
Meclizine does help in dizziness and the eustachian tube blockage / middle ear problem can cause imbalance and may sometimes cause the symptom. So taking these medications is good first step towards the therapeutic diagnosis and I would agree to the treatment.