If you intend to enter a professional school after graduating with your bachelor's degree, we would refer to you as "pre-professional."
Pre-Law is a designation for those who seek admission to law school. There is no list of set courses required for law school. Instead, law schools want to see students who have developed strong communication and analytical skills.
Pre-Health is a designation for those who seek admission to health professional programs, usually upon completion of a bachelor's degree. Many pre-health students are interested in becoming a doctor, pharmacist, physician's assistant, physical therapist, occupational therapist, dentist, or veterinarian.