It looks like opportunistic fungal infection due to oral thrush or candidiasis in your case. I would advise you to get a swab sample of the white coating and then starting with antifungal drugs after consulting an ENT surgeon.
Itchy skin can be due to dermatitis,dry skin, scabies and hives, internal diseases like liver and kidney disorders,diabetes, iron deficiency anemia, irritation and allergic reactions to chemicals,wool,soaps and cosmetics.
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. He/She will start with the specific medications. 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 doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.