Swimming on Shabbos

Swimming in a river is prohibited on Shabbos since you may come to make a raft (בונה). The mechaber rules that swimming in a private pool is prohibited for the same reason. The Mishna Brurah writes that if the water doesn't reach the top of the pool, it's permitted. However, he writes that the minhag (based on the Terumat HaDeshen and others) is not to because you may come to wring out your towel or clothing.

The psak of Rav Moshe Feinstein.

What about showering on Shabbos?