If it itches use benadryl to dry it up. Otherwise use a good face cleaner and this should work for your back as well.
Hi, welcome to the forum, the tiny spots on the skin other than acne, suggests atopic dermatitis which is seen due to allergic background and Contact dermatitis due to direct skin exposure to a substance which can be a allergen or irritant.
Anti-histamines with appropriate steroids against prescription will help to alleviate the condition. Identify and avoid the triggering factor which you been exposed to recently.
I suggest you to consult a dermatologist for further management. Take care and regards.