Discover is notorious for looking at the whole picture other than just a simple credit score. They are also not known for giving generous credit lines - even to those whose scores and history are in far better shape than yours. I've seen people with your score get discover cards, but not very often. I've never seen anyone (at least here on MyFico) who is 20 years old with 17 open and relatively new accounts, with more than a dozen inquiries on their reports get a Discover card - even those like you who seem to use what you have responsibly. Don't be in such a rush. Mellow out a bit and let what you have grow for a while. In all honesty, (I assume you're looking for a truly honest assessment) I wouldn't apply for anything for five years. More isn't necessarily better. Believe me, I know!
Just trying to give you advice here....not trying to tell you what to do.....
I really think you should ask yourself why you're addicted to credit (credit cards)?
Wrap up all your cards in a rubber band and stick them in your dresser drawer and don't use them for 3 months.
Then ask yourself what you were thinking?
If you keep up with this behaviour at 20, you're risk for charging off by 27 is about 93%.