Internships are an important way for you get professional references, add depth to your design portfolio, and get experience working with design teams. In an internship, you may find you are working with people who may hire you when you graduate or who will provide references and professional contacts to you.
Packaging design is often considered a specialization of industrial design, and sometimes is offered as a separate program.
It is becoming more common for employers to require a master's degree for entry-level work in the field.