Stroke: This is the most likely diagnosis given the combination of symptoms. Bells palsy can be a presentation of a stroke, especially if it's a lacunar stroke affecting the brainstem or a larger stroke affecting the facial nerve. Dizziness and dysphagia are also common symptoms of stroke, particularly those involving the brainstem or cerebellum.

Multiple Sclerosis (MS): MS can present with a wide range of neurological symptoms, including facial weakness (similar to Bells palsy), dizziness, and dysphagia, due to demyelinating lesions in the central nervous system.
Acoustic Neuroma: Although less common, an acoustic neuroma (a benign tumor on the nerve connecting the inner ear to the brain) can cause facial weakness, dizziness due to its effect on the vestibular nerve, and dysphagia if it compresses nearby structures.
Lyme Disease: Neurological manifestations of Lyme disease can include facial palsy (often bilateral), and less commonly, symptoms like dizziness and dysphagia, especially in the context of Lyme meningitis.

Brainstem Infarct: A stroke in the brainstem can cause a combination of these symptoms and is critical to diagnose promptly due to its high morbidity and mortality.
Cerebellopontine Angle Tumor: Tumors in this location, such as meningiomas or schwannomas, can compress the facial nerve, vestibulocochlear nerve, and lower cranial nerves, leading to the symptoms described.
Multiple Cranial Neuropathies: Conditions like Guillain-Barré Syndrome can cause a range of cranial neuropathies, including facial weakness, and can also lead to dysphagia and dizziness.

Sjögren's Syndrome with CNS Involvement: Although rare, Sjögren's syndrome can have central nervous system involvement, leading to a variety of neurological symptoms, including those described.
Tolosa-Hunt Syndrome: This rare condition involves non-specific inflammation of the cavernous sinus or superior orbital fissure and can cause facial pain, ophthalmoplegia, and occasionally, symptoms that might mimic those described.
Melkersson-Rosenthal Syndrome: Characterized by recurrent facial paralysis, swelling of the face and lips, and the development of folds and furrows in the tongue (fissured tongue), it could be considered in the differential, especially if there's a history of recurrent facial paralysis.