Game design is not an easy position to get into in the games industry. Depending on the game, it might be a more math intensive job than you are prepared to do. It is often done by the president of a small company, or by a singular person on a small team.
A large company will need a very specialized designer. And junior jobs are highly contested and difficult to get into.
Instead of going to school for game design. Go to school for computer science. Learn statistics, and learn excel (google spreadsheets). Know how to take data and analyze it. Learn how to figure out percent chances of complicated randomness. Be a mathematician.
Practice drawing every day. Practice with a mouse using shapes with google draw. Take a drawing class. Learn how to do pixel art. Learn how to do line shading. Learn how to do simple 3D modeling. Do that instead of going to school for game design.
Learn how to program. Learn how to create a prototype. Create practical prototypes of game ideas when its faster than programming something. Watch youtube videos like Mark Brown's gamemaker's toolkit. Do that instead of going to school for game design.
Then go to school for anything. Anything at all. I still suggest computer science. But if you're more art oriented you can attend a technical school for that. Even history is fine. Just don't go for game design. Have insanely good grades. You do not want a C average. Also go to a really good school.
After all this, you can have a very good chance of being hired for a game design position. But you'll find what most people who get a game design degree learn: if you want to be a game designer, you have to do it yourself. Being an indie is the way up. At which point you're going to want to learn about business and advertising.
You have to do it yourself. A game design degree won't get you there. It might help you with some of these tools, but it won't be extensive enough in any field. You're going to have to learn a lot of this on your own. I suggest going to learn the things that are hard for you to learn. And self study the rest.