Based on the symptoms and history provided, the following differential diagnoses are considered:

Single most likely diagnosis
- Chlorine-induced asthma or reactive airway disease: This is the most likely diagnosis given Jennie's symptoms of a dry hacking cough that worsens with swimming in a pool. The chlorine in the pool can trigger asthma symptoms or reactive airway disease, especially in individuals who are prone to respiratory issues.
Other Likely diagnoses
- Allergic rhinitis: Jennie's history of frequent colds (four to five a year) could suggest an allergic component, and her symptoms might be exacerbated by allergens such as chlorine or other pool chemicals.
- Vocal cord dysfunction: This condition can present with a dry cough and can be triggered by irritants such as chlorine. It's more common in young women and can be associated with respiratory symptoms that worsen with specific triggers.
Do Not Miss (ddxs that may not be likely, but would be deadly if missed.)
- Pulmonary tuberculosis: Although less likely, it's crucial to consider infectious causes of chronic cough, especially in individuals who may have been exposed to tuberculosis. A missed diagnosis could have severe consequences.
Rare diagnoses
- Hypersensitivity pneumonitis: This is a rare condition caused by an allergic reaction to inhaled substances, which could potentially include pool chemicals. It's less likely but should be considered if other diagnoses are ruled out and symptoms persist.

To further evaluate Jennie's condition, the following diagnostic tests could be ordered:

Spirometry: To assess lung function and diagnose asthma or reactive airway disease.
Methacholine challenge test: If spirometry is normal, this test can help diagnose asthma or reactive airway disease by assessing airway responsiveness.
Allergy testing: To evaluate for allergic rhinitis or other allergies that might be contributing to her symptoms.
Chest X-ray: To rule out other pulmonary conditions such as tuberculosis or hypersensitivity pneumonitis.
Vocal cord function assessment: If vocal cord dysfunction is suspected, a referral to an ear, nose, and throat (ENT) specialist for laryngoscopy might be necessary.

These tests will help narrow down the differential diagnoses and guide appropriate management for Jennie's condition.