This is the first tournament that I played without my school chess club, and my first individual USCF rated tournament.  I was part of a three way tie for first in my group of five people, scoring 2/3. 

Any analysis of the games would be appreciated, but more importantly I'm wondering if anyone can tell me what I need to do to improve; that is, what parts of my game are weakest and how can I work on them?  I would really appreciate any advice you can offer.

I've fully annotated the games, and analysed parts with the chess engine Crafty.

I was happy with how I played in round 1, I don't think I made any blunders, but a few mistakes and inaccuracies.

I thought that I played a good middlegame in round two, but major mistakes in the opening and endgame lost the game for me.

My last game was very poorly played from both sides, my opponent and I both missed some very elementary stuff.

Thanks for any advice you can give!

If I was you, I'd learn different openings, especially for black.  Check out this rather informative thread (especially the second post) regarding good black openings for lower rated players.  A rock solid opening leads to a decent middle game.

Spending some time with the tactics trainer would get you to see the traps laid for you as well as help you lay a couple yourself.

http://www.chess.com/forum/view/chess-openings/good-positional-opening-for-black-against-e4-and-d4

In game one you played sharply and well, although your opponent gave you plenty of help! But you were aggressive and tactically sharp. I have to agree with the computer that 9.Bxf4 and 11.Qd3 were both a bit better than the moves you selected, but in both cases, your choices were also good moves. Well done, but you need stiffer competition.

Game two must have been disappointing, but you should remember what happened to you on move 7. This kind of trap/blunder happens more often that you might think, where the pinned Bd7 offers only imaginary protection. But you fought back well (with a little help) and equalized the game. You missed a chance to equalize with 28....g5! but he gave you a second chance when he didn't play 29.Rh1, so you ended up with an equal game anyway. It's a pity that time trouble changed the game into a farce at the end, but you could have preserved a winning edge with 46...Rd2+ followed by Rb2. It's worth reviewing that, so you will recognize the pattern easiliy the next time you're in time trouble.  Two quick points: There was no need to take that e5 Knight on move 6. ^...g6 was a good alternative. And 7...a6 was strong for you

As you say, game 3 was the most error-filled, but this isn't uncommon in the last round. You're young, but you were still probably tired at the end of a long day. Still, you made the next to the last error, and that's what it takes to win. I didn't like your 6...f5. One of your opponent's few assets is the Bb2. By weakening yourself on the long diagonal, you run the risk that his Bishop could be a valuable weapon. You also weaken your King position a little and delay your development. Although White certainly doesn't have any real compensation for a pawn, he is slightly ahead in development. If he had played 7.Bd3, I think he would have have some real compensation in the form of a lead in development.  I think 6.Nf6 is simple and strong: You develop a piece and get ready to castle. I think this was  the only strategic mistake you made.