Redness comes from blood flow or internal bleeding, which is a possibility after bad carpal tunnel surgery.
Dry palms are usually due to the layer of dead skin cells on the palm. The dead skin cells may also contain dead tinea corporis. Check to see if the dry skin is also cracking. If there is cracking, then there would be live tinea corporis present. Wash the hands with warm and hot water and a lot of soap vigorously and frequently. Then wash the hands with a lot of hydrogen peroxide frequently. This will alleviate internal blood accumulation, remove the dead skin cells, and kill the bacteria and fungi on the skin that may be the causes of the dry palms.