What causes a person to be sweating one minute and shivering the next?

Answer 1

That person may be suffering from chills.

Chills AKA Rigor is defined as:

Rigor is a shaking occurring during a high fever. It occurs because cytokines and prostaglandins are released as part of an immune response and increase the set point for body temperature in the hypothalamus. The increased set point causes the body temperature to rise (pyrexia), but also makes the patient feel cold until the new set point is reached. Rigor occurs because the patient is effectively shivering in a physiological attempt to increase body temperature to the new set point.