I never get over how quickly flyer talkers attack the OP.
Public shower - like in the middle of the street? Get real!
Walk to your room dripping sweat over everything and looking disreputable? Double get real - and poor form.
Privacy in a shower in a Female Washroom (or Male for that matter) is important and should be fully secure. The hotel staff member made a mistake and the OP is entitled to reasonable compensation. I am surprised that the manager was reasonably generous.
It was a valid question and occasionally answered politely and properly.