Migraine with Aura: This condition is characterized by headaches that can be accompanied by a variety of neurological symptoms, including auras that can manifest as burning sensations or visual disturbances. The pattern following the circle of Willis and the presence of ringing in the ears (tinnitus) could be part of the migraine aura or associated symptoms.

Tension Headache: While typically less severe than migraines, tension headaches can cause a band-like pressure around the head and could potentially be accompanied by tinnitus, though the burning sensation might be less common.
Temporal Arteritis: This condition involves inflammation of the blood vessels in the head and can cause headaches, though it's more common in older adults. However, it could potentially cause a burning sensation and tinnitus due to the inflammation affecting various structures.
Sinusitis: Inflammation of the sinuses can cause headaches and facial pain, and in some cases, might be accompanied by tinnitus due to Eustachian tube dysfunction or referred pain.

Subarachnoid Hemorrhage: Although less likely given the chronic nature of the symptoms, a subarachnoid hemorrhage (bleeding into the space surrounding the brain) can cause sudden, severe headaches and could potentially lead to symptoms that might be interpreted as a burning sensation. It's crucial to rule out this condition due to its high mortality and morbidity.
Giant Cell Arteritis: Similar to temporal arteritis but can affect larger arteries, including those in the circle of Willis, potentially leading to severe complications like stroke or blindness if not promptly treated.
Meningitis: Inflammation of the protective membranes covering the brain and spinal cord, which can cause severe headache, fever, and sometimes tinnitus or a sensation that could be described as burning.

Trigeminal Neuralgia: A chronic pain condition that affects the trigeminal nerve, which can cause intense pain or burning sensation in parts of the face, though it's less likely to follow the circle of Willis pattern or cause tinnitus directly.
Cerebral Venous Sinus Thrombosis: A rare condition where a blood clot forms in the brain's venous sinuses, which can cause headaches, though the pattern and associated symptoms might vary widely.
Vestibular Migraine: A type of migraine that can cause vertigo and potentially tinnitus, but the burning sensation and specific pattern following the circle of Willis might be less typical.