Numbness on one side of the brain along with headache, more with movement of the neck can be due to whiplash injury or cervical spodylosis.
Diagnosis can be confirmed by X-ray, CT or MRI of the head and neck.
You can use anti-inflammatory painkillers like ibuprofen, paracetamol. Muscle relaxants, or narcotics will also help. Use of soft cervical collars is also helpful. A good posture may help. Brace your shoulders slightly backwards, and walk 'like a model'.