Thanks for using Healthcaremagic,
You have been diagnosed Hypothyroidism
recently, I presume you have already started supplementation of Thyroxine
Dry, itchy skin is very common feature of hypothyroidism which may be responsible for itching, but other differentials must be considered like Urticaria
that is allergy if there is redness and raised skin patches and related to particular exposure.
Dryness of skin due to dehydration
and lack of estrogen Menopause?.
Infection of fungus would be another possibility.
If dryness is there using moisturizers should help or taking anti allergy medicine to see if it helps.
Hypothyroidism may take some time before improvement is seen and depends how severe is condition.
If troublesome please visit a Dermatologist
to find out exact cause and treat it accordingly.
Hope this helps.