こんにちは!
ご質問ありがとうございます。
ご質問について、いくつか言い方が考えられますが、『[承認欲求](https://eikaiwa.dmm.com/uknow/questions/62460/)』は、a desire for acceptance というように表現できます。受け入れられたい・認められたいという願望というニュアンスですね!
また、ご質問内にある文章は、以下のように表現できます。
Japanese often face criticism from their parents growing up, which can seriously impact how they see themselves. It can be challenging for them to be themselves on social media; they tend to seek approval from others. It's as if they're lost, uncertain of their true identity, and any negative feedback from people outside their close circle can easily hurt them.
参考になれば幸いです。