If you web search for annual ryegrass control in wheat, there will be some recommended herbicides for treatment. I have never tried any of them. I have a horrible problem. It just really showed up one year. I buy combine run wheat for planting - and that is probably where it came from.
You live in north carolina I am assuming here. You got plenty of time to hit it with clethodim. IT will kill the wheat and has a 2-3 week residual. But, could put down winter rye after that.