First off, I am not an expert at all. I have just picked things up from general lurking.
To clarify: A game designer does not make games. He (or she) is the person who decides that Steve should give you the garlic so you can defeat the vampire. A game designer would not have any part in physically making the game. A game developer is a general term that includes both game design and game programming.
Second off, you seem to think that taking a course is the only way to make games. This is wrong. I am not even out of high school (or equivalent of, I'm just 16) and have been making games for 4 1/2 years in my spare time. You would want to consider this a lot further than 'I like games'. There's a hell of a lot more to it than that. Actually try and create something first, and see if you're still into it then.
I'm not entirely sure for game design exclusively, but for game development/programming:
There is very, very little point in getting a specific degree. Not only is the industry very competitive, there are few places. Say you've graduated from uni. However, you can't get a place at a game studio and you can't get one at a software place since they want a computer science degree. Bit stuck now?
It is almost always better to go for a more general degree rather than something incredibly specific in a case like this, where the specific is a subset (i.e. a CS degree will help you greatly for any programming job; a game dev degree won't)
Currently you have not posted anything. Edit your post and click the < > button to give you code tags and paste between those. That, or the code formatting is being sorted right now.
Either that, or you're expecting us to rate the code without actually giving us code.
And to post work into your profile you need to become a GD.NET+ member. It costs money for the subscription, but you get a dev journal and space on here for projects and support the site. If you've only just written your first project, it may be a little much (unless you want to support the site).