How can I get into a video game career?

You've done a good job of summarizing the challenges. You are right that it's a brutally competitive field, because so many people want to get into it. The good news is, you really don't need any special education. Video game companies are looking for one thing alone: work samples which prove you have talent. And you can get started right away, by creating storyboards, mod'ing, etc. Good luck!