Viral Upper Respiratory Infection (URTI): Given the age of the patient, the symptoms of cough and runny nose, and the presence of sick contacts at home, a viral URTI is the most likely diagnosis. These infections are common in infants and are often transmitted through close contact with family members.

Bronchiolitis: This is a common lower respiratory tract infection in infants, often caused by respiratory syncytial virus (RSV). The symptoms can start with upper respiratory tract symptoms like cough and runny nose before progressing to wheezing and distress.
Allergic Rhinitis: Although less common in infants as young as 2 weeks, exposure to allergens could potentially cause symptoms similar to a viral URTI.

Congenital Heart Disease with Respiratory Symptoms: Infants with undiagnosed congenital heart disease can present with respiratory symptoms due to pulmonary overcirculation or congestion. Early diagnosis is crucial for management and outcome.
Inborn Errors of Metabolism: Certain metabolic disorders can present with nonspecific symptoms including respiratory distress. Early identification is critical for treatment.
Bacterial Infections (e.g., Pneumonia, Sepsis): Although less likely given the initial presentation, bacterial infections can rapidly progress and become severe in newborns. They require prompt recognition and antibiotic treatment.
Pertussis (Whooping Cough): Especially if there are known contacts with pertussis or the infant is too young to have started or completed the pertussis vaccine series, this diagnosis must be considered due to its potential severity in young infants.

Cystic Fibrosis: Presents with recurrent respiratory infections, but diagnosis at 2 weeks of age would be unusual without other significant symptoms like failure to thrive or gastrointestinal symptoms.
Primary Ciliary Dyskinesia: A rare genetic disorder that affects the motor function of cilia, leading to recurrent respiratory infections. It's unlikely to be diagnosed at this age without a family history or other suggestive symptoms.
Chronic Granulomatous Disease: A rare immunodeficiency that could lead to recurrent infections, but would be unusual to present with such nonspecific symptoms at this age without other signs of infection or failure to thrive.