South Carolina’s jobless rate reached a new high in January. The South Carolina Employment Security Commission reported Wednesday that the unemployment rate was 12.6 percent in January, up from a revised 12.4 percent in December. Almost all major categories lost jobs in January, with the biggest loses coming in retail, leisure and hospitality, and government work. Retail cut 7,700 positions in January as temporary workers were released after the holiday season. Construction lost another 1,700 jobs. The number of the state’s unemployed rose by 4,600 to a state record of more than 273,000. Unemployment rose in all of the 46 counties. Allendale and Marion Counties tied for the state’s highest jobless rate at 24.3 percent. Unemployment was lowest in Lexington County at 9.4 percent.