I don't know what Oxford dictionary says. I imagine this situation: you badly bumped into a pillar. Your friend is worried. He says: "Please have a look at your leg. You may have hurt yourself." meaning: you may be hurt without being aware of it in the first moment.

It it always helpful to provide more context. Practical English Uage gives "Polly is very late. She may have missed her train." [3rd edition section 339.8] In North American English, the following are interchangeable. She may have missed her train. She might have missed her train. She could have missed her train. Also, there is a stronger form when the speaker is certain. She must have missed her train. She has to have missed her train.

Which Oxford guidelines? Can you provide a link?

That sounds correct to me.

But As per oxford guidlines it is wrong to use may/might for the past possibilities with the known outcomes. Only could can be used. So,it is correct in American English.Isn't it? Intresting. Thank you!