Dental Abscess or Infection: Given the patient's history of complex dental caries, a dental abscess or infection is a highly plausible cause for the facial swelling, especially considering the firm area lateral to the nose which could indicate a localized infection or abscess formation.

Cellulitis: Facial cellulitis could present with soft tissue swelling and might not always be accompanied by fever, especially in early stages or in immunocompromised patients. The firm area could be an indication of a more localized infection.
Dentoalveolar Abscess: Similar to a dental abscess, a dentoalveolar abscess could cause localized swelling and firmness, particularly if it involves the teeth or surrounding bone near the area of swelling.
Parotid Gland Infection or Abscess: Although less common, an infection of the parotid gland could cause facial swelling and might be considered given the patient's complex medical history.

Ludwig's Angina: A severe infection of the submandibular space that can cause significant swelling and airway compromise. It's crucial to consider this diagnosis due to its potential for severe complications, including airway obstruction.
Cavernous Sinus Thrombosis: Although rare, this condition can arise from facial infections and has a high mortality rate if not promptly treated. The presence of Moebius syndrome might increase the risk of complications due to potential craniofacial anomalies.
Orbital Cellulitis or Abscess: If the infection spreads to the orbit, it could lead to serious complications, including vision loss and intracranial infection.

Eosinophilic Granuloma (Langerhans Cell Histiocytosis): This rare condition can cause localized swelling and might be considered in the differential diagnosis, especially if other causes are ruled out and there are systemic symptoms or other signs suggestive of Langerhans cell histiocytosis.
Hemangioma or Vascular Malformation: Although typically present at birth or shortly after, a hemangioma or vascular malformation could potentially cause facial swelling, especially if it becomes infected or undergoes rapid growth.

Clinical Examination: A thorough examination of the oral cavity, face, and neck to assess for signs of infection, abscess, or other abnormalities.
Imaging: Consider CT or MRI scans to evaluate the extent of the swelling and to rule out deeper infections or other causes.
Laboratory Tests: Complete blood count (CBC) to look for signs of infection, and blood cultures if there's suspicion of bacteremia.
Dental Evaluation: Consultation with a pediatric dentist to assess the dental health and potential sources of infection.
Antibiotics: Empirical antibiotic therapy may be started based on the suspected cause of the infection, with adjustment based on culture results.
Surgical Intervention: May be necessary for drainage of an abscess or management of other complications.
Airway Management: Close monitoring and potential intervention for airway protection, especially if there's concern for Ludwig's angina or other conditions that could compromise the airway.