If you always try to please everyone, you'll lose yourself in the process.
気を使う→please someone
そんなに気を使ってばかりいたら、あなたがあなたらしくいられなくなっちゃうよ→If you always try to please everyone, you'll lose yourself in the process.
lose yourself→あなたらしさがなくなる
in the process→やってる間に(気を使ってばかりしてる間に)
If you're always worrying about everyone else, you won't be the person you were meant to be.
この場合、次のような言い方ができますよ。
ーIf you're always worrying about everyone else, you won't be the person you were meant to be.
「いつもみんなに気を遣ってばかりいると、あなたがなるべき人でなくなるよ」=「あなたがあなたらしくいられなくなるよ」
ご参考まで!