Viral upper respiratory tract infection (URTI): This is the most common cause of dry cough and low-grade fever in infants. The symptoms are typical for a viral infection, which is often self-limiting and common in this age group.

Bronchiolitis: Caused by respiratory syncytial virus (RSV), it's a common lower respiratory tract infection in infants, presenting with cough, fever, and sometimes wheezing.
Pneumonia: Bacterial or viral pneumonia can present with cough and fever. The low-grade fever might suggest a viral etiology, but bacterial pneumonia cannot be ruled out without further investigation.
Allergic rhinitis: Though less common in infants, it could present with dry cough due to postnasal drip.

Congenital heart disease: Though not directly causing cough and fever, undiagnosed congenital heart disease can lead to respiratory symptoms due to heart failure. It's crucial to consider in any infant with unexplained or persistent respiratory symptoms.
Cystic fibrosis: An inherited disorder that can cause respiratory and digestive problems. Early diagnosis is critical for management.
Tuberculosis (TB): Though rare in infants, TB can present with chronic cough and low-grade fever. The risk is higher if there's exposure to an infected individual.
Pertussis (Whooping cough): Highly contagious and can be severe in infants, presenting with a characteristic whoop sound during coughing spells, though this might not be evident in early stages or in very young infants.

Foreign body aspiration: Can cause sudden onset of cough and respiratory distress. It's less likely if the symptoms have been present for a long time but should be considered if there's a history suggestive of aspiration.
Anatomical abnormalities: Such as tracheoesophageal fistula or laryngomalacia, which can cause chronic cough and respiratory issues.

The treatment will depend on the final diagnosis. For the most likely diagnosis of viral URTI, treatment is supportive:

Acetaminophen (paracetamol) for fever: 15 mg/kg/dose every 4-6 hours as needed.
Saline nasal drops for nasal congestion.
Hydration and monitoring for signs of dehydration or worsening respiratory status.

For other conditions, treatment will vary:

Bronchiolitis: Supportive care, with oxygen therapy if necessary. Ribavirin may be considered in severe cases or high-risk infants.
Pneumonia: Antibiotics if bacterial, supportive care for viral.
Allergic rhinitis: Antihistamines or nasal corticosteroids.

It's essential to consult a pediatrician for a thorough evaluation and specific treatment recommendations based on the diagnosis.