Designer here.
If you don't already have some skills and aren't 100% sure that you want to be a designer, then pick something different.
If you are serious, then I would suggest doing a two year program or minoring in GD, and majoring in something relatable like Marketing, Business or Communications. You will be a far more valuable asset if you can prove that you bring more to the table than the ability to make pretty pictures.
I wouldn't say that Graphic Design is a dying career, but it is definitely evolving. You can't really be just a print designer anymore, and it seems a lot of schools are slow on realizing this. You need to be able to code or illustrate or do motion graphics. Employers aren't looking for one-trick ponies, they want someone who can do everything.
Everyone in here is making a big deal about salary, but they don't really get the industry. Median salary for a GD is 30-40k depending on where you look. Not amazing for a recent grad, but not terrible either. However, after 5-10 years, if you are good at what you do, you should be able to move into an Art Director position. Median salary 70-80k. There is also the availability of extra income through freelance work, which can be pretty lucrative, $50-200/hr.
I knew going into it that I wasn't going to be swimming in cash, but I'm very happy with where I am, and what I've experienced because of my decisions. I've worked with professional athletes, dined in all the dopest spots in the city, seen the best live music, and am currently doing work with some of the biggest companies in the action sports world. Not bad for someone just a couple years out of school.