Don't know for sure if it is the cause, but my advice would be to back off the weight until you can handle it without the wraps. I used to use wraps all the time (which I guess means I went heavy all the time) and I had a lot more joint problems and injuries. Since ditching the wraps (I only use them occasionally for super-heavy days), I have had the same results and my grip has improved remarkably. You may find that you don't have to drop the weights all that much, especially of you use a mixed grip.
What might be happening is that the weight is so heavy that it is pulling your arms and shoulders down too much, which may tend to pull the rib cage away from the sternum. In any case, I think it is an indication that the weight is causing a serious stress on your bones, tendons, and ligaments, and it could easily lead to a serious injury. Probably not a big deal occasionally, but I wouldn't think that can be good on a regular basis.