How can I tell whether knowledge is true or false? Why do I care about the truth of knowledge?

First of all, you should know why you don't trust others. You don't believe what others told you because there is no authority? Still not convincing to you?

Secondly, why not choose another way of thinking? You can choose not to believe what others say. No one is asking you to live according to what others say. Since you can't prove that they are right or wrong, don't prove it, just do what you believe. Do what you like and ignore what you don't understand.