But I learned my lesson - no showering - or even undressing in any public place. Period. When I work out, I'm dressed from head toe, and I wait until I get home to bathe & change. No changeroom, no shower.
This also depends on the gym that you go to. I have been going to the same gym for almost 30 years. 2 different locations. Personally never had any problem, neither has anybody else that i know there. We regularly use the steam rooms and the showers etc. One place we all stay away from is the whirlpool. Although the temperature is considerably high, but who knows what lives in the water there. The jets can very easily be used as a communal bidet.
Unless you are extremely shy, go ahead and enjoy all the amenities at your gym. That way it will become a pleasant experience, instead of a chore.
Just my 2 cents.