You can't use "whether" in that sentence. It is 100% correct as it is. You can say: ".....I don't know whether he will pay it back." or "......I don't know whether he will pay it back or not." "Whether" implies an alternative. In your sentence, you are certain.

you can also use whether ，but the sentence should be "I am afraid whether he will forget to pay it back or not."

Thank you Eliot!

No, you can't.