The most likely cause of your itching hands and feet is an allergy. It could be an allergy to medications, food, something that has touched your hands and feet, such as soap, etc.
I suspect that the most likely cause of such an allergy reaction is the Tylenol #4, which contains codeine. Codeine is closely related to morphine. You can develop an allergic reaction to a medication after some time of using it without difficulty.
Any of your other medications might have caused the allergic reaction, but it's difficult to know without stopping the meds and seeing if the itching disappears.
I would recommend stopping the tylenol #4 and trying to get by with just tylenol. Benadryl can be bought over the counter, and should help. I would use benadryl 25mg 1-2 3 times daily as needed. It can cause drowsiness.
I'm not aware that Familial Mediterranean Fever causes hand/foot itching, although it may be a possibility that there is some relationship.
If stopping the codeine doesn't give you relief within a couple of days, or if you develop any other symptoms, I would contact your doctor. Best wishes.