Internships are a good start. Since as of now you are working as an intern ,so make sure that you start developing your own portfolio. Your portfolio should reflect who you are are.

Fashion industry works on recommendations. Working as an assistant to an stylist helps you to learn the very basics and at the same time helps you to build useful cantacts. Getting a bachelor's degree in  in fashion merchandising will also help you make connections, score internships and, ultimately, get hired. you'll learn about design trends, product development, marketing, manufacturing and more.

One important thing is maintaining a helathy relationship with your superiors. This alone can help you to find work in the fashion industry and establish your career.

Good luck