If the skin on your mother's hands and feet is red, irritated, and has sores, she likely has a condition called hand-foot syndrome, also known as palmar-plantar toxicity. Hand-foot syndrome
is a reaction that occurs with certain chemotherapy drugs when they leak into the tissues of the hands and feet, causing irritation and inflammation of the tissues. The swelling, peeling and blisters and can be very painful. If your mother has this condition, it's important to tell her doctor right away. The doctor may choose to decrease her chemotherapy dosage or postpone a chemo treatment.
Have your mother ice the sore skin and ask her doctor if it's okay to use cortisone ointment. Also make sure she avoids washing dishes in hot water or putting pressure on her hands by squeezing tools. There some small studies that suggest that taking vitamin B6 at a fairly high dose (50 to 150 mg) can help, but again you should discuss this with her doctor.
This condition is not the same as neuropathy, which is nerve damage (also from chemo) and causes tingling, numbness, and a pins-and-needles type of pain.