Dawson's 19th Arkansas and the Portlocks 24th Arkansas were not around Corinth in May of 1862. The 19th Arkansas had just returned for the Indian Territories and were recruiting in their home counties before moving to Camp White Sulphur Springs in June and the 24th Ark. was being organized there in July and August 1862.
The parts of the 19th and 24th Arkansas that became part of the Army of Tennessee did not get there until after April 1863 when they were exchanged from prison after the fall of Arkansas Post.