"管好自己和他人"的英文表达方式有几种,具体如下:

Take care of oneself and others
这个表达方式是指注意自己和他人的健康和安全,也可以指注意自己和他人的情感和需要。例句:
Please remember to take care of yourself and others during this pandemic.
As a parent, it's important to take care of yourself and others in your family.
Look after oneself and others
这个表达方式也是指注意自己和他人的健康和安全,但是强调的是对自己和他人负责任,并在必要时给予帮助和支持。例句:
As a caregiver, it's important to look after oneself and others to avoid burnout.
It's everyone's responsibipty to look after oneself and others in the community.
Take charge of oneself and others
这个表达方式指负责自己和他人的健康和安全,并承担相应的责任和义务。例句:
As a leader, it's important to take charge of oneself and others to ensure the success of the team.
Parents should take charge of themselves and their children's safety and well-being.

以上三种表达方式的来源都是英语的常用语,可以在日常生活和工作中使用。