Viral Upper Respiratory Tract Infection (URTI): This is the most common cause of the symptoms described, often resulting from viral infections such as rhinovirus, coronavirus, or adenovirus. The presence of headache, nasal congestion, and sore throat without cough is typical for many viral URTIs.

Allergic Rhinitis: This condition can cause nasal congestion, headache, and sore throat due to postnasal drip. The absence of cough does not rule out allergic rhinitis, as cough is not a universal symptom.
Sinusitis: Both acute and chronic sinusitis can present with headache, nasal congestion, and sore throat. The headache is often worse in the morning and can be exacerbated by bending forward.
Influenza: Although influenza typically includes cough, some cases may present with headache, sore throat, and nasal congestion without a significant cough, especially in the early stages.

Meningitis: Although rare, meningitis is a life-threatening condition that can initially present with headache, sore throat, and may have associated nasal congestion due to the inflammatory response. A high index of suspicion is required, especially if the headache is severe and accompanied by fever, stiff neck, or altered mental status.
Temporal Arteritis (Giant Cell Arteritis): This condition can cause headache and may have associated systemic symptoms such as fever and sore throat. It's more common in older adults and can lead to serious complications like vision loss if not promptly treated.
Lymphoma or Other Malignancies: In rare cases, lymphoma or other head and neck malignancies can present with symptoms similar to those of a viral URTI, including sore throat and nasal congestion. A persistent or worsening course of symptoms despite typical treatment should raise suspicion.

Granulomatosis with Polyangiitis (Wegener's Granulomatosis): A rare autoimmune disorder that can affect the respiratory tract and kidneys, presenting with a variety of symptoms including nasal congestion, sore throat, and headache.
Sarcoidosis: This condition can affect multiple parts of the body, including the lungs, skin, and eyes, and may present with nonspecific symptoms such as headache, sore throat, and nasal congestion due to granulomatous inflammation.
Tuberculosis: Although more commonly associated with cough and systemic symptoms, tuberculosis can present atypically, especially in immunocompromised individuals, with symptoms such as headache, sore throat, and nasal congestion due to extrapulmonary involvement.