I hope I don't get injured and just stay healthy this year.
I hope I don't get hurt or sick this year.
この場合、次のような言い方ができますよ。
ーI hope I don't get injured and just stay healthy this year.
「今年は怪我をしないで健康な年であってほしい」
ーI hope I don't get hurt or sick this year.
「今年は怪我や病気をしないといいな」
ご参考まで!