score:8
Hmmm, this is tricky.
First, there are flights you paid for but didn't take. You may be able to get a refund for that and you should certainly get the (some of) the taxes back for the untaken return flight.
Because your cancelled return flight was due to the fault of an agent working for American it is right that they should have made arrangements to get you back to the US. However, as I understand it, there's no requirement for them to do this in any given time -- they can give you the next flight with seats, although I believe they should pay accommodation / food for the extra stay (although that might vary with country). Unfortunately you turned this down, which probably released them from their obligation -- I'd guess the money for the return ticket is gone -- since you legitimately gave the money to a different airline you're not going to get it back.
What follows assumes that you were correct the original flights were legit and the agent made a mistake forcing you to change. If the agent was right then AA still screwed up when they changed flights, but they tried to make it right as best they could, and I think the best you can hope for is some sort of refund on the return flights you didn't take.
However, if you can definitely prove the initial flight should have been OK then you have a better argument for the initial screw up. They made a mistake and cost you money, then it looks like you have a good argument that you were incorrectly 'upsold' or forced to buy something you didn't need. I would contact local authorities and/or the Better Business Bureau. I would make the argument that you were missold something and explain you want your 1500 back plus compensation (or punitive damages).
Secondly, there is nothing wrong with making a big deal of this -- but, as the comments above say, just don't come off like a jerk. That means you need to accept that you turned down (even accidentally) the valid return offer and concentrate on the misselling. It does sound like much of the staff were friendly too you, so also accept that and highlight those you feel were unprofessional. As long as you're calm and reasonable, and accept where you may have not helped the situation, I wouldn't think it counts against you in the long run.
How to make a big deal? I'd be surprised if AA don't Google themselves, so someone in customer services may find your post or this question but you could post a link to either with a brief note 'very disappointed in AA' to their twitter feed (@AmericanAir). Or their facebook. Or even try and get local news to pick it up, "struggling student loses thousands of dollars" might make the news on a slow day.
If you paid any of this on credit cards check what if they have built in insurance, it's possible that they might be prepared to give you some of the money back.
But the charge for the return flights is legit, and there's no way you can challenge that or get it back from the airline you used. You need AA to stump up compensation.