
I'd look first at possible allergens as has been said - food, cleaning products (including laundry), maybe even environmental outdoors but that one's harder to pin down.
Then thyroid, although unlikely at only 6 months old - but certainly not impossible.
It could possibly be a form of alopecia too - not sure what westies are prone to specifically beyond bad skin, but some types of alopecia can start early. My dobe boy has had it from day dot, his is a hereditary type called colour mutant alopecia - not something seen in westies, it's to do with the dilute genes that cause fawn or blue coats in dobes (mine's a fawn), also seen in weims, and blue dogs of some other breeds IIRC. So he won't have that, but just to give you an idea of the sort of thing that could be happening.