Can I sue a visiting nurse?

No, you cannot effectively sue:
First, if you have a conservator, the nurse may have to report to him about what you are doing: these depends on the conservator's authority, what actions you are taking, what the nurse is "squealing" about, etc. We don't know if this is the case, but mention it because depending on the exact facts, since the conservator has a duty or responsibility to/about you and authority over your life/situation, it is not necessarily inappropriate for the nurse to relate certain facts to him.
Second, there is no protection against "gossip": while certain medical  information may be protected by HIPPA rules, legally a nurse can relate what she sees you doing, watching, spending money on, etc. It may be inappropriate and unprofessional, and you may be able to file an ethics complaint with the nursing licensing board or with any hospital or agency which supplies her, but it's not something you can sue over.
Third, a lawsuit is generally for compensaton for actual losses or damages you suffered, not just having your life made "difficult." If you have not suffered some financial loss or other quantifiable harm, there is no compenstion to which you'd be entitled in a lawsuit.