Breathing discomfort, similar to after swimming in chlorinated pool. Normal? Pulse ox/basic labs/ BMI good.

Dyspnea. If you are having difficulty breathing you should definitely go and be evaluated by a doctor. Hope this helps.
Shortness of breath. More information is needed. Do you have known allergies? Are you a smoker? Was a chest X ray or pulmonary function test done? It is unclear if this is a reactive airway condition and what is causing it. Get a second opinion if you did not have a thorough evaluation.
No. If you are describing mild shortness of breath it may be related to mild bronchospasm. The way you relate it to inhaled chlorine makes me think that you have been exposed to something similar. Symptoms are suggestive of mild reactive airway disease.