Start with programs like Python, C++ or Java to get a good understanding and continue to branch out and learn other paths and programs out there. Getting a Bachelors Degree in Computer Science is going to benefit you a hell of a lot more than a Bachelors in Game Design. Trust me.
Once you have a good grasp of coding, start branching out to game engines that you can tinker with to learn how to make games. Unreal Engine, Unity and Godot Engine are some of the many engines you can tinker with. RPG Maker is great for dipping your feet into overworld creation, story boarding and stat balancing for characters and enemies.
Keep learning, keep creating, and keep improving. Good luck out there.
Hope this helps !