If you are considering a particular vocation, ask someone now doing that job for time to discuss that with you. The short answer is that the most traditional route is to become a therapist first, then specialize in sex therapy second.
Most states have licensing for social work and for psychology.
Licensed Clinical Social Worker. Master of Science usually doesn't. At the doctoral level, you earn a Ph.D. in Psychology, Educational Psychology, Counselling Psychology, Clinical Psychology, or Education. To get a doctorate in psychology without doing a dissertation you get a Psy. The route I have just described pretty much requires experience in the broad spectrum of psychological problems.