The insignia you describe is colored red and blue.The details you describe are blue and the background is red.The insignia is for the 30th Infantry Division "Old Hickory".
The division was named after famed president and soldier Andrew Jackson. Born near the North / South Carolina line and rising to fame in Tennessee, he provided the regional flavor to this tightly knit group of soldiers. The division's patch is an obvious link to this heritage being an "O" and "H" with the Roman numeral XXX in the middle. Interestingly , the patch was worn horizontally during World War 1. Local folklore has taught that a Raleigh tailor inadvertantly placed the patches horizontally and others just copied what they did not know was incorrect.