@SarahGen-- You should not exfoliate frequently if you have dry and sensitive skin. Once a week sounds right in your case. People with oily, problem skin can exfoliate up to three times a week. So it depends on the individual.
We all have different types of skin based on hereditary factors. Some people have thicker skin and they have a hard time getting rid of dead skin cells. Exfoliation is more important for this type of skin. If dead skin cells are not removed regularly, skin will look dull and it might cause acne.
Also, pick the right type of exfoliating face wash. Some scrubs are formulated for sensitive skin and they have soothing, moisturizing ingredients like oatmeal and natural oils.