Viral Bronchiolitis: Given the patient's history of recurrent bronchiolitis, current symptoms of wheezing, cough, and crackly chest sounds, along with a recent episode of fever that has settled, viral bronchiolitis is the most likely diagnosis. The patient's age and clinical presentation are consistent with this condition.

Asthma: Although less likely given the patient's age, the recurrent nature of the symptoms and the presence of a family history of eczema (which is associated with atopic diseases like asthma) make asthma a consideration. However, a definitive diagnosis of asthma in an infant is challenging and typically requires a pattern of symptoms over time.
Reactive Airway Disease: This condition can present similarly to asthma and bronchiolitis, with symptoms triggered by viral infections or other irritants. The patient's history of recurrent respiratory issues and current symptoms could fit this diagnosis.
Pneumonia: Although the patient does not have a high fever or significant distress, pneumonia should be considered, especially given the history of recent illness and the presence of crackly sounds on lung exam.

Pertussis (Whooping Cough): Despite the absence of a "barking cough," pertussis can present atypically in infants, and the cough can be severe and persistent. Given the potential severity and the importance of public health implications, pertussis should be considered.
Foreign Body Aspiration: Although less likely given the chronic nature of the symptoms, foreign body aspiration can cause recurrent or persistent respiratory symptoms and should be considered, especially if there's any history suggestive of an aspiration event.
Congenital Heart Disease: While the patient's symptoms could be primarily respiratory, congenital heart disease can sometimes present with respiratory symptoms due to pulmonary congestion. Given the patient's recurrent admissions for bronchiolitis, ensuring that cardiac causes are ruled out is crucial.

Cystic Fibrosis: This genetic disorder can cause recurrent respiratory infections and symptoms similar to those presented. Although it's less likely without other suggestive symptoms like failure to thrive or gastrointestinal issues, it remains a consideration in the differential diagnosis of recurrent respiratory problems in infancy.
Immunodeficiency: Conditions that affect the immune system can lead to recurrent or severe infections, including respiratory infections. The patient's history of recurrent bronchiolitis admissions could prompt an evaluation for an underlying immunodeficiency, although this would be rare.