Swimming pool 也为pool， an area of water that has been created for people to swim in。
She trained five times a week at her local swimming pool.
上面是从牛津词典上查到的，一个是对swimming pool 的英文解释，在解释中是用in； 下面那句话是给的例句，却是用的at。这样看来，in 和at都应该是对的，如果是in的话可能是紧接着swim的，考虑pool的话，用at搭配。
这个还是问下老师吧，老师说考试的时候算对的那个就记住吧