You can't compete.
You can't compete with his teammate, with the hours of time they spend together. You can't compete with his passion for the sport, a passion they clearly share. You can't be one of the guys the way she can. Somehow, she walks the line of "one of the guys" and "obvious girl" with a grace you've never seen and you know you can't compare to that.
You can't compete with a bender, not only that, but also a Firebender. There's a shared bond between them. You can see it when they practice Firebending forms together. They move as one, an ancient and long known dance that they know. You watch and know that you can never be a part of that. Oh, sure you can learn the moves, and you can spar with him in your own way, but he'll insist on fighting on even terms. He can't spar with you without having to hold back, but with her, he can be the natural adversary he was born as.
You can't compete with his friend. True, she's only known him a few weeks more than you, but they've already formed a strong bond. They've fought Amon together, they've competed in the Pro-Bending Tournament together. What have the two of you done together? You've gone to fancy dinners and been to your house, but none of that has formed any strong bond like they have. She was smart enough to discover the truth about your father, the truth that you never realized even though you lived there, and she discovered it in days. What have you done?
She's not just some girl.
She's his teammate.
She's his friend.
She's smart.
She's noble.
She's the Avatar.
You're just some girl who hit him with a moped.
You're just some fan girl from the arena.
You're just a traitor's daughter.
You're just some rich girl.
You're just you.
And you can't compete with her.