grammar - "Could not but"

(I posted this on English learner's group, but no one gave an answer. I hope this is a more appropriate group to post this question.)

Is the following sentence grammatically right to write in literature?

How could I not but close my eyes?

As "I could not but close my eyes" is a valid sentence, I felt like this one should also be valid. But I am confused whether 'could not but' can be used like that in interrogative sentences.