I've heard that expression while I was in Beijing, and I can't find the translation when I scroll the Internet. Do you know what it means?
In Chinese, 红眼(red eyes) always mean someone is in extreme emotional state.
So combing with 急(anxious\angry), it means you are so anxious that your eyes turn red.
他急红了眼(He's very very anxious or angry)
You can try more combinations, like 哭(cry)
他哭红了眼(He's very sad)
他愁红了眼(He's very worried)
他杀红了眼(He's on killing spree)
In theory, you can add 红眼(red eyes) to many verbs, but in reality, only a few verbs are allowed to do this.
急红了眼 means being very anxious or angry. I think it's a regional slang but I can't find a dictionary entry to this exact phrase.
I have found two very closely related (and synonymous) words: 急眼 and 红眼, the former of which is slang. The reference to "red eyes" indicates strong emotion, where the eyes can become reddened especially when one is on the verge of tears.
But the phrase prefers to express someone is about to do something so badly that he wouldn't care about any (usually terrible) consequences. Considering 红眼 also has the meaning of envy, jealous.
So violated, fictional not real