Its been about nine years since I've had a bad hangover, and my last one was a doozy, but as I remember, the dizziness at the tail end of a hangover isn't too different from anxiety dizziness. My guess is you started out with hangover dizziness, which caused you some anxiety which caused anxiety dizziness, and the two blurred together.
The amount that you drank, while it would ruin the next day for me, isn't really a huge amount for a college student. Since you don't drink much, I'm not surprized you didn't feel well the next day, but you shouldn't be brain damaged. I knew a guy in college who once did thirty shots of tequila in one sitting, and survived without brain damage (well, not from the tequila anyway, he was an idiot to begin with) He also weighed about 220, so I don't recommend normal people trying this.
You might want to go to the doc to see if you hurt your head falling, just in case, but it doesn't seem likely. You might also want to mention the anxiety. I don't know how student health centers are about giving things like xanax for anxiety - that seems like abuse waiting to happen, but you can see. It could confirm that your dizziness is just anxiety. In the long run though, you'll want to find a way to deal with the anxiety. I recently started seeing a therapist - something I probably wouldn't have considered at 19, and something I should have done four years ago. You might have counseling services available for low cost through your university. I would seriously recommend that you look into it - you don't have to tell your friends. Anxiety is no fun, and the sooner you deal with it correctly the better. I know the young male mentality - I used to be one - but the desire to tough it out on you own is probably not the best option.
BTW, stop drinking Keystone - Ugh!