Can peroxiding your hair make you sick?

There is no such thing as "peroxiding your hair". You likely mean "bleaching your hair with peroxide". Bleaching your hair means using a chemical to lighten the color of your hair. Peroxide is one of the chemicals that can be used for this purpose. It works by breaking down the melanin in your hair, which is what gives your hair its color. Bleaching your hair can cause some damage to your hair, but it is not known to cause any serious health problems. However, if you are allergic to peroxide, you may experience some skin irritation or other allergic reactions.