This fic carries a sweet sentiment and it's nice to see the tie-back to the very first episode.
However, there are quite a few kinks in this fic that need ironing out.
1. The song lyrics. Very copy/paste and it could have been *any* song. You could have copied and pasted 'Hit Me Baby One More Time' and it wouldn't have made any difference. There's a reason you picked the song you did, right? Make sure it comes across in your fic.
2. Katara going capslock on Aang.
"Katara snapped, 'WHAT’S WRONG? YOU ARE LEAVING AGAIN. EVER SINCE YOU DEFEATED THE FIRE LORD, WE HAVE BARELY SPENT ANY TIME TOGETHER. YOU’RE ALWAYS TOO BUSY. YOU EVEN FORGOT TODAY IS THE ANNIVERSAY OF OUR FIRST KISS!'"
Trust the reader to know that Katara is angry. And trust your own writing ability - you *can* carry across tension, hurt, and anger within dialogue without using all caps.
(Also: You missed an 'r' in anniversary. Just a silly type-o, but I thought you should know.)
3. Neither Aang or Katara ever *said* anything. They sighed, they snapped, etc. It's really all right to use the dialogue tag 'said'. You won't be impaled for it. I promise.
4. The descriptions of setting were decent, but when trying to describe what was going on with Katara internally, the writing felt very vanilla.
Ex.
"However, Katara, who loved Aang with all her heart, was often depressed. Aang and Katara admitted their feelings for each other, but after the war, Aang was often too busy to talk, and Katara was scared that Aang didn’t love her anymore."

Show, don't tell. It's boring to just be told flat-out that a character is depressed, is scared, etc. *Show* the reader that Katara is depressed. *Show* the reader why. How does Katara move? How does she speak? What does she say? What do other characters say to her? How do *they* speak? How does her feeling depressed affect her day to day activities, like teaching water bending? Does she become distracted easily, stare off into space, have difficulty smiling, etc?
All these things can easily convey to the reader that Katara is feeling down in the dumps without blatantly telling the reader.

Over all, this wasn't terrible, but there is room for improvement. Keep writing! Practice makes perfect!
-Folk Ballad

Aww! this was so cute! hey, can you you check out my new story? it's called "Like Whoa" and I'm not getting much reviews