From your symptoms of skin itching without any rash and dryness in the eyes, one possibility is of allergies or atopic dermatitis. Oral antihistamine, such as Benadryl can be used to relieve itching. 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. He/She will start with the specific medications. If an internal disease is found, whether it's kidney disease, iron deficiency or a thyroid problem, treating that disease often relieves the itch. Lastly, Phototherapy can also be tried.
If still the symptoms do not improve then please get a clinical examination done by a dermatologist. Other possibilities like internal diseases like liver and kidney disorders,diabetes and iron deficiency anemia need to be ruled out.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your dermatologist. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.