Is it normal to be burned severely during chemo and radiation?

This is a concern you need to discuss with your mother's doctor. Radiation burns do, regrettably, occur sometimes during radiation treatment for cancer. Sometimes doctors know in advance that this is likely, based on the location of the cancer and the type and dosage of radiation used, and plan ahead to treat the burns. (For example, patients having radiation to the head and neck are told to prepare for radiation burns.) You might say it's an unavoidable side effect. Other times it isn't supposed to happen but does because the calculations used to determine the radiation dosage are very sensitive and it's possible to miscalculate.  

But if your mother had previously had radiation therapy without severe burns and is now experiencing burns, it seems likely that this isn't what the doctor intended. It's also possible that with the addition of chemotherapy, the burns are not healing as fast as they were before. Your mother needs to call her doctor right away and describe the location and extent of her burns as clearly as possible. (Or you may wish to call for her.) The doctor can prescribe treatment, and will also pass the information along to the radiation oncologist and staff so they can recalculate the dosage before the next appointment.