Am I allowed to stay in the country if I am getting married 2 weeks before my J-1 Visa expires?

Marriage will not, by itself, extend a J-1 visa. Marriage may, however, be a basis for eligibility to apply to adjust status to become a Lawful Permanent Resident (to get a "Green Card"). Significantly more information is needed in order to provide a legal analysis. This includes, for example, information about your spouse's own immigration status (a U.S. citizen?), information about any two-year home residency requirement associated with your J1 visa, etc. There really is no substitute for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.