I’ve been wearing braces. I’ve been wearing braces.

That's fine but I think most people would say "I wear braces." or "I have to wear braces."

I’m happy that my teeth are becoming straighteneding up, but it is uncomfortable when eating. I’m happy that my teeth are straightening up, but it is uncomfortable when eating.

A pPieces of rice and ramen noodles often get stuck behind my braces. Pieces of rice and ramen noodles often get stuck behind my braces.

Since you're talking about something that often happens it's better to use the plural for both types of food.

I learned that I should eat curry the day before the day when exchanging my braces because mythe rubber attachinged to the ceramic brackets turn to yellows from a clear color to yellow. I learned that I should eat curry the day before exchanging my braces because the rubber attached to the ceramic brackets turns from a clear color to yellow.

I encounter a lot of difficulties during wearing braces, but I’m looking forward to the day when I come off my bracesan have them taken off. I encounter a lot of difficulties wearing braces, but I’m looking forward to the day when I can have them taken off.

Melty cheese isn’t alsoalso isn't good because it sticks behind them and it was hard to get the cheese out. Melty cheese also isn't good because it sticks behind them and is hard to get out.

After I had eaten a croissant, it covered most of my brackets were covered with it. After I ate a croissant, it covered most of my brackets.