I have 2 westies, both with skin conditions, Its very common within the breed, What are you feeding her/him, most westies have skin allergies due to wheat/gluten, To start with if the dog was mine i would start on a hypoallergenic diet, as in james well beloved, it is a dry mix, but if your dog is not used to that pets at home do a tray of hypoallergenic wet food that you can mix the james wellbeloved with to wean them over (butchers is gluten and weat free but made mine sick) It does definately take up to 6 weeks for the itching to subside if this is the problem, but in my experience it has mainly been, You can help your dog with 1 piriton human tablet (cetrizine) 1 a day check with your vet, but it should be fine plus dog washing weekly in polytar shampoo...human for skin conditions and soriosis, buy at boots not cheap.....mind you non of it is when you have a westie.
good luck
jo.