My wife gets respiratory infection when she goes to hometown- wheezing, not able to climb stairs and bouts of coughing. is it ashthma or dust allergy?

Sounds like both: The more time spent around particular allergens, the more allergic to them you can become. She grew up exposed to whatever is in her hometown, and thus may indeed have developed allergy. Asthma can be thought of as an allergic reaction in the lungs. Allergy alone can cause a cough, but the wheezing is likely asthma.

Asthma maybe dust: Sounds like asthma which may be triggered by something in the hometown environment. This could be due to dust although the dust in your current town would be expected to cause the same thing. Albuterol may provide temporary relief.