The word cringe was used as an action for someone experiencing pain. "The needle hurt so much he cringed in pain." It was then used to express that a situation was so embarrassing it was painful. So painful is the right translation in this case.
I agree with your conclusion, but I don't think the etymology makes your point, because I was predicting the Japanese term used that-- depending on context-- is translated as "cringe" or "embarrassing".
My error was that I didn't realize that I was proposing a bringing to the forefront the underlying meaning of his words (in truth, it's that
I'm 99.9% sure he truly is alluding to the matter of "cringiness" and "embarrassment") when he's regardless talking about "pain". Indeed, it wouldn't make sense to render, say,「 痛い!視線が痛い!」with the intention of using the term "cringe" or even "embarrassment" to carry the sense of 痛い. "Their gazes are [embarrassing]" may work given the next clause where he corrects himself on what's "painful", but me arguing for that would be more me salvaging my original position.