Is it normal to have chills, shivering and nausea during menstrual cycle? Severe cramping as well?

Can be. Prostaglandins are released when the uterine lining breaks down. They are a nasty group of chemicals that cause fever, chills, nausea, diarrhea, and pain. This can be treated with prostaglandin inhibitors such as naproxyn or ibuprofen which work best if started at least a day before your period starts or with contraceptives which decrease the amount of lining there is to break down or with both.