Why not apply to an MBA directly next year if your long-term goal is to get an MBA? 3-4 years of working experience would help as well. Public sector is not that bad as long as you have some leadership or project management experience. Some top B-schools actually like to recruit students from public sectors to improve their diversity. The most important thing is to find out what you really want to do and then incorporate your ideas into the essays in order to convice adcom.