It sounds like your vet took the lazy way out. I agree with billboo that this sounds more like an allergy issue. Because it seems to coincide with your new baby, I wonder if your dog is allergic to one or more of the baby products now in the house? Even talc in baby powder can cause dermatitis.
No doubt your house is turned upside down with the arrival of the new baby (congratulations by the way!) and your Westie's routine has likely been a good deal different. If he isn't getting walked like he once did, or not having play time, maybe you can hire a teenager to take him for a spin every day. Dogs are like babies: they respond very well to a set schedule that includes sleeping, eating and playing. Upset that schedule too much and problems crop up.
Hi there, I have two Westie's but no kids and both my dogs do what your dog is does due to allergies. My girl Westie has an allergy to grass which during certain seasons it makes her lick her feet until the fur is all pink and the skin is raw. She started doing this when she was around 2 and still has this problem mildly at age 4. I have helped with this problem by when she has flare ups I wash her feet everyday with a shampoo called "Malaseb" & giving her homapathy drops for grass allergies. The vets said the same thing to me when she first started doing that she was stressed but i knew there was more to it. My boy dog I adopted in Oct 07 and at the age of 1.5 had no fur on his paws, armpit and throat area when I got him. He also has an allergy which i'm still trying to get to the bottom of but with antibiotics and rubbing the diluted malaseb on every second day this has helped with him scratching and biting. Perhaps you should ask your vet about it been an allergy? Hope this helps. Betsy & Billys Mum