I wouldn't say that charge cards or specifically AmEx charge cards are particularly hard to get, it's just that they demand quite a high criteria. For example excellent payment and credit history, a certain level of household income etc.
Personally, I don't find it difficult to control my spending on cards and so it's probably easier for me to build up a good credit history as a result. I haven't missed a payment and pay off my statement in full whether it be a credit or charge card. I'm sure this helps my credit score.
I'm 20, so not much older than the OP and have AmEx's Platinum Charge Card. I knew I didn't have a poor credit history when I had the Green Card, but I was a bit surprised when AmEx invited me to become a Platinum Cardmember.
If I were you, I'd carry on building up your credit history by using other cards (sensibly!) and then re-apply in a year. I don't think you'll have a problem getting a Green card then if you have a good credit history.