Without reviewing your lease and examining the scene, I cannot give you a definitive answer. However, if you think your landlord is treating you unfairly, you should consult an experienced landlord/tenant lawyer in your area.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
It depends if the shower has been constructed on the common area of the apartment complex. If you are actually paying rent on the space that contains the shower, then, no - the landlord cannot tell others that they can come onto your rented property to use anything. If the situation is one where you put up the shower without the express permission of the landlord on common area property, you may have no rights to insist that it is yours alone. What does you lease agreement say about the shower or use of the common areas?
Is this new behavior by the landlord? If so, you may have an argument that would grandfather the private use of the shower. If the landlord is new, or he/she has previously complained about the shower, your chances for success are lessened. If the use of the shower by others is disturbing your quiet enjoyment of your unit, you may also argue that issue. Seek the advice of a landlord/tenant attorney to help you sort out what your rights and remedies may be.
Carol Johnson Law Firm, P.A. : (727) 647-6645 : firstname.lastname@example.org : Wills, Trusts, Real Property, Probate, Special Needs: Information provided here is anecdotal and should not be relied upon or considered legal advice. Every matter is different and answers given here are general in nature and may not reflect current Florida law at the time you are reading this posting. Please contact me if you feel you need additional assistance with your matter.