Viral Upper Respiratory Tract Infection (URTI): This is the most common cause of throat pain, nasal pain, and headache. The symptoms presented are typical for a viral infection such as the common cold or influenza, which often include sore throat, nasal discomfort, headache, and sometimes tooth pain due to sinus pressure.

Sinusitis: Given the nasal pain and burning, along with headache and teeth hurting (especially in the upper teeth), sinusitis is a plausible diagnosis. Sinus infections can cause pain in the face, headache, and toothache due to the involvement of the sinuses.
Streptococcal Pharyngitis (Strep Throat): Although less common than viral URTI, strep throat is a significant cause of throat pain and can be accompanied by headache. It's essential to consider this diagnosis due to its need for specific antibiotic treatment.
Allergic Rhinitis: If the symptoms are seasonal or triggered by specific allergens, allergic rhinitis could be a diagnosis, causing nasal pain, burning, and headache due to congestion and sinus pressure.

Meningitis: Although rare, meningitis is a life-threatening condition that can present with headache, fever, and sometimes throat pain if there's associated pharyngitis. It's crucial to consider this diagnosis, especially if the patient has a severe headache, fever, or signs of meningismus.
Temporal Arteritis (Giant Cell Arteritis): This condition, more common in older adults, can cause headache and jaw pain (which might be referred to the teeth) and is a medical emergency due to the risk of vision loss.
Ludwig's Angina: A severe infection of the tissues in the neck, which can cause throat pain, difficulty swallowing, and sometimes tooth pain. It's a medical emergency due to the risk of airway obstruction.

Dental Abscess or Infection: While not the first consideration given the combination of symptoms, a dental abscess could cause localized pain that might be referred to the throat or nasal area, especially if the infection spreads.
Trigeminal Neuralgia: A condition that affects the trigeminal nerve, causing intense pain in the face, which could be mistaken for tooth pain, nasal pain, or headache. However, the pain pattern is typically more episodic and severe.
Sarcoidosis: A systemic disease that can affect multiple parts of the body, including the sinuses and lymph nodes in the neck, potentially causing the symptoms described. However, it would be an unusual initial presentation.