Where are you located? Most places in the US are looking for designers where the entry level positions are at minimum a 4 year degree and 2 years of real world experience. Get those 2 years while you are a student in any way you can, whether it’s internships or part time jobs. Don’t turn down production work either. You could learn a lot working for a printer, sign shop or custom build house.
Because you already have a bachelors, you may have to negotiate doing a second major for a bachelor of arts in design. Just about any college is going to want a solid 3 years of your tuition money even though you might be able to complete the course work in 2 years. But don’t be afraid to negotiate. About the last thing you want as a starting designer is a Masters in design. You can do that later if you feel the need (and more often these days it’s done in a complimentary field, not more design.) At least you’ll have your core courses done.
If you aren’t in the US, your mileage may vary.
The field is over-saturated already and if I were to counsel a pre-college graphic design candidate, aside from maybe considering a different career path, it would be to find a niche in the design field and work toward it right from the start. Don’t just do “graphic design.” Do you want to do web? Print? Marketing? Animation? Show biz in any or all of its forms? Environmental design? Experiential design? Industrial design (including UI/UX)? You have to get out beyond the design-for-a-dollar crowd to make a living at it these days. Explore your options now. Don’t wait for that senior year thing.