I am self-diagnosed AND a teenager and I have something to say on this subject.
I did not diagnose myself because I was depressed at a certain time- yes I become depressed and anxious a lot but they are short-lived and generally, I'm not sad the majority of the day. I came upon the subject of AS on wikipedia. I was reading about genetics... and one of the pages led me to autism... I thought that although I was very bad at social situations, had obsessions, unnecessary movements as my mom puts it (nail-biting, rocking, running, etc), and sensitivity to some things, I did not have any speech delay. Then as I scrolled through the page I came across AS. When I read it, I put a %5 chance that I might have it. The next days I searched for autism and AS as well as genetics in search engines. I read a LOT of pages with symptoms and took a few quizzes... but even now, while my level of certainty about having AS is very high, it is not 100%... I know a lot about psychology, neurology and other things that can cause social differences and oddities, and out of them, AS seems to best describe my type of oddity. However my knowledge in this area isn't complete. I know a lot, but I don't know everything.
I think that the chances of a formal diagnosis being correct is higher than a self-diagnosis, but they both have a chance of being right; or wrong. I think it cannot be known for certain, for a 100% chance that someone has AS or not until a fundamental difference in the genetic or cerebral make-up of Aspies and NTs is discovered, one that applies to everybody. If I am tested one that way, one day, if it turns out positive, it'll show that my self-diagnosis was right; if it turns out negative, I'll start reading every psychological and neurological book until I find something else that can describe me.
But, until that happens, I find AS to explain me better than anything else I know about.