My asthma-like symptoms that developed after swimming in pool cleared up quickly on ventolin/advair. does this mean they are definitely due to asthma?

Likely: Most likely this is from asthma. And you are better, a good thing. Methacholine challenge testing is a "gold standard" for asthma. You want to discuss this with your lung doc.

Not necessarily: The right trigger will make anyone wheeze. If you have no prior lung issues, then it was likely a reactive bronchospasm which may have had an allergic or chemical trigger since were at pool. Will need a recheck in a couple weeks with pulmonary function test to see if resolved or ongoing impairment.