Hi, I can understand your concern for itching on arms and back that quickly bleed on scratching. There can be multiple possibilities of your concern but I can make a possibility of either scabies or Allergic dermatitis . In Allergic dermatitis there are eruptions along with moderate itching and in more aggravated cases there is appearance of more redness which persist for more than multiple of days. In scabies the red lesion and dry lesions are present and typically there is night itching. The only precaution you must follow is not to touch, pinch pop or squeeze any of them other wise it can get infected and can cause complications. If I were your treating then would have prescribed permethrin 5% cream followed medium potency steroid cream application such as mometasone or fluticasone cream. You can take antihistamine benadryl or loratadine by mouth. Take care.