Sinusitis: This condition is characterized by inflammation of the sinuses, which can cause headaches, facial pressure (including maxillary pressure), and neck stiffness due to referred pain and inflammation.

Tension Headache: Often presents with neck stiffness and headache, though maxillary pressure is less common. It's a frequent cause of headache and could be considered if the maxillary pressure is mild or intermittent.
Migraine: Can cause severe headaches, neck stiffness, and sometimes facial pressure, including maxillary pressure, especially if the migraine involves the trigeminal nerve.
Cervicogenic Headache: Originates from the cervical spine and can cause neck stiffness and headache. The maxillary pressure could be referred pain from the cervical spine.

Meningitis: Although less common, meningitis is a critical diagnosis that must not be missed. It can present with severe headache, neck stiffness (often more pronounced than in other conditions), and fever. Maxillary pressure is not a typical symptom but could be present if there's significant inflammation or if the condition has led to sinusitis.
Subarachnoid Hemorrhage: A severe condition that can cause sudden, severe headache (often described as "the worst headache of my life"), neck stiffness, and sometimes facial pain due to the involvement of cranial nerves.
Temporal Arteritis (Giant Cell Arteritis): Can cause headaches, facial pain (including maxillary pressure), and jaw claudication. While neck stiffness is not a primary symptom, it could be present due to pain referral.

Trigeminal Neuralgia: Characterized by sudden, severe, shock-like pain around the eyes, lips, or nose mainly because of the irritation of the trigeminal nerve. It could cause maxillary pressure and, less commonly, neck stiffness if the pain radiates or if there's associated tension.
Occipital Neuralgia: Involves the nerves that run from the base of the skull to the scalp and can cause pain that feels like a sharp, stabbing, or electric shock-like sensation. While primarily causing scalp pain, it could lead to referred pain in the neck and face, including maxillary pressure in rare cases.
Rheumatologic Diseases (e.g., Rheumatoid Arthritis, Lupus): These conditions can cause a wide range of symptoms, including headaches, neck stiffness, and facial pain due to inflammation and autoimmune responses. Maxillary pressure could be part of the symptom complex if there's involvement of the sinuses or facial structures.