Is this a good skincare routine for a 13 year old?

At night:
wash my face with Cetaphil Gentle Skin Cleanser
Apply Panoxyl 10% Benzoyl Peroxide Foam every other night (perscribed by dermatologist)
Moisturize with either Cetaphil Moisturizing Lotion or Cetaphil Moisturizing Cream

Morning:
i just rinse my face with water( is that bad? i don't want to over wash my face because the Benzoyl Peroxide irritates my skin)
moisturize my face with Aveeno Positively Ageless spf 35 Moisturizer (for sun protection)
i try to be super gentle because i am very young but since i have acne i have to take care of my skin