There are many possibilities for such an itchy skin without any rash. It can be due to psoriasis, dermatitis, lice, scabies and hives, internal diseases like liver and kidney disorders, diabetes, iron deficiency anemia, irritation and allergic reactions to chemicals, wool, soaps, cosmetics and certain foods .
You can apply an anti-itch cream or lotion to the affected area. Oral antihistamine, such as Benadryl can also be used. You should take a comfortably cool bath and wear smooth-textured cotton clothing. You should choose mild soaps without dyes or perfumes and use a mild, unscented laundry detergent when washing clothes, towels and bedding.
Please take a second opinion from a dermatologist if the symptoms persist.
I hope it helps. Take care and regards.