Asthma: This is the most likely diagnosis given the combination of wheezing and dyspnea. Asthma is a chronic inflammatory disease of the airways characterized by recurring episodes of wheezing, coughing, chest tightness, and shortness of breath. The presence of a dry cough and wheezing are hallmark symptoms.

Chronic Obstructive Pulmonary Disease (COPD): COPD can present with similar symptoms, including a chronic cough, wheezing, and dyspnea, especially in smokers or those with a history of exposure to lung irritants.
Bronchitis: Both acute and chronic bronchitis can cause cough and dyspnea. While wheezing is less common, it can occur, especially in chronic bronchitis.
Pneumonia: Although typically presenting with a productive cough, some forms of pneumonia (like viral or mycoplasma pneumonia) can cause a dry cough, wheezing, and significant dyspnea.

Pulmonary Embolism: Although less common, pulmonary embolism can present with sudden onset dyspnea and may be accompanied by a dry cough and wheezing in some cases. It's critical to consider this diagnosis due to its high mortality rate if untreated.
Cardiac Failure: Heart failure can lead to pulmonary congestion, causing cough, wheezing (cardiac asthma), and significant dyspnea. It's a condition that requires prompt recognition and treatment.
Pneumothorax: A spontaneous pneumothorax can cause sudden dyspnea and may be associated with a dry cough and wheezing. It's a medical emergency that needs immediate attention.

Cystic Fibrosis: While more commonly diagnosed in childhood, cystic fibrosis can present in adulthood with respiratory symptoms including a chronic cough, wheezing, and dyspnea due to bronchiectasis and recurrent infections.
Eosinophilic Pneumonia: A rare condition characterized by an accumulation of eosinophils in the lungs, which can cause cough, wheezing, and dyspnea.
Sarcoidosis: An autoimmune disease that can affect the lungs, causing a variety of symptoms including cough, dyspnea, and less commonly, wheezing.