Olá Andréa! Bom Dia! Segue a minha correção do seu texto. Espero ter sido útil!
Título: What is your favorite sport?
My favorite (sport) is volleyball.
(I have) played it since (I was) twelve years old. I started to play at school during (break) (1) and at P.E. class (2).
I participated in competitions at school (and) won some medals, (which) I still keep.
Nowadays, I still play volleyball. I play on Thursdays and Saturdays. On Thursday nights I play in XXXX, and on Saturdays I play in YYYYY.
On YYYYY, the game is more fun because the people (who play there) aren't as competitive (as the ones) in XXXX, (who) just want to win.
(I used to play) in SSSSS on Fridays. (It was) very fun (to play there, too). I stopped playing there because (now) I study (on) this day.
I love to play volleyball because it’s very fun. Volleyball is also a great exercise (and) it has developed (my) teamwork (3).
(1) Break (intervalo) é a forma mais usada para se referir ao tempo entre alguns dos períodos de estudo;
(2) P.E. class, ou Physical Education class, é como se refere a aula de Educação Física;
(3) Sugestão, para caso você esteja se referindo aos benefícios do esporte: "About its benefits, volleyball is a great exercise and helps to develop teamwork".