It might be a bit extreme but if you have any old, light clothing you don't mind ruining you could wear them to shower?

We had to use outdoor shower blocks on camping trips back in school and they basically said 'no nudity' so it was washing in a throw away outfit or don't wash.
It's awkward and far from perfect but it's do-able and if it's effecting you THAT badly then it might be an option worth trying at least?

Hope you can find some relief from it somehow Dorothy :(

If you work out a method that works I'm sure more then a few people on BC would be interested in the details.
You're not alone :)

Nessa