I have spots on my chest and back and shoulders antibiotics didn't work what could it be?

Allergy . Could be an allergic reaction to something. Food, clothing, soap, or anything you may have come into contact with. You can try taking otc Claritin (loratadine) tabs to see if it improves. If it does then find out what is causing this allergy and try to avoid it in the future.
Did you receive vacc. Could be seborrhic keratosis. I have seen recently people who received flu vaccine having skin eruptions. The other reason could be atopic dermatitis - due to allergens - have this tested you can use otc Hydrocortisone cream if it is due to chemicals doing a liver detox will help elimiate toxins have this checked out.