It is unlikely to be a condensation issue with paint peeling, although this is possible. I would suggest in the first instance that the plumbing be inspected to ensure that there are no leaks from the water pipes or wastes. If no leaks are detected then condensation may be responsible. In this case you would likely require an electrician to ensure that the shower room is correctly ventilated using an extraction device.
Peter Barber CSSW.,CRDS.
Structural Waterproofing Surveyor.