There is an article by Rabbi Michael J. Broyde and Avi Wagner in
Journal of Halacha & Contemporary Society 39; Spring 2000 – Pesach 5760 in which they argue that in America, showering on Yom Tov might be permitted. The article is available online. I ran their logic past a rav and he agreed with the logic so I have always showered on Yom Tov.
Relevant excerpt from the article:
“It is possible that there is no custom to refrain from bathing and showering in cold water on Yom Tov; However, even a person with a clear custom not to bathe or shower on Yom Tov, who is uncomfortable on Yom Tov – because of the heat or because of uncleanliness – is permitted to shower on Yom Tov, rather than to spend Yom Tov feeling uncomfortable. One who is ill certainly may take a hot bath or shower on Yom Tov, if that will make him feel better. There appears to be no more of a reason nowadays for a sick person to take a cold shower than a hot one, given that bathing in hot water is clearly shaveh lechol nefesh. It should be noted that when showering or bathing or even only washing the face, one must be careful not to squeeze water out of one’s hair, nor use solid soap.”