game design is a terrible career path. its incredibly competitive and doesnt pay well as a result. everyone says "i want to make video games!" and is willing to work for practically nothing just to get their foot in the door.
if you are actually a skilled programmer, you'll make far more money and get a job far more easily in software development than in game development. the job market is oversaturated with people who think making video games is as easy as playing them.
btw, i am a graduate student in computer science, if that adds anything to my opinion on the matter. i've talked about game development with professors (some of whom know people working in game development) and some of my own friends working in game development. i have not heard a positive thing about it. make absolutely sure it is what you want to do with your life before going down this path.