First I want to wish you luck with this new med! But also some comments...
If your doc is a stick in the mud about prescribing... you may simply want to ask him if it is ok for you to take an OTC antihistamine - like Benadryl, to see if it resolves the itching.
Other things can cause itching, besides allergies, so i do think it is worth investigating. if the Benadryl does not resolve it, it might be good to do labs - complete blood workup CBC, electrolytes, liver panel and urinalysis. Want to make sure there isn't something else systemic going on - and if there is to get you off the drug before it becomes dangerous.
My hope is that it a transient reaction. I hope it is not an allergy because it isn't a good idea to stay on Benadryl continuously. But rule out allergy and your labs are clean, then quite possibly this itching could be transient and you will feel ok within a few weeks.
I wish you well with this med... 21 AEDs is a lot to burn... i'm wracking my brain trying to name that many!
((( gentle soothing anti-itchy hugs )))
~ waves ~