I'm currently on sick leave from work, but I haven't told my parents about this. I don't want them to worry.
I don't want to trouble them.
I don't want them to get anxious about me.
ご質問ありがとうございます。
① "I'm currently on sick leave from work,"=「私は現在、病気で休職しています」
"but I haven't told my parents about this."=「でも、両親にこのことは伝えていません。」
"I don't want them to worry."=「彼らに心配して欲しくないので。」
② "I don't want to trouble them."=「彼らに迷惑をかけたくないので。」
③ "I don't want them to get anxious about me."=「私のことで不安になって欲しくないので。」
ご参考に。