I agree with Barb, you should switch medicine to different brand and then see if you are still itching.
It's possible that you are having a reaction to the fillers. Ask your doctor if you can switch to Tirosint, which is a gel cap; better absorbed and hypoallergenic because it has no fillers.
It's worth a try, though some people find that they have to lower their dosage of Tirosint because of the better absorption.