没事 别担心 不要紧 没关系 别害怕 别慌

directly translate "don't worry" to chinese is "别担心（bie dan xin）”

不要紧 or 没关系。

不要紧！is correct. It is a very good phrase! But it is also very oral and informal. To use it in a formal way, for example, in a business setting, you should say 没有关系！／不用担心！