This is a common symptom of allergies in dogs.
Paw licking and skin chewing is often a sign of allergies. You may see red staining to the fur in the licked areas or raw spots where the dog chews itself to the bone.
The skin itches from allergies, the dog licks and chews trying to soothe the itch, making the skin raw and allowing other infections to set in which may itch even more.
It is believed that the chewing of the dog's own flesh releases chemicals in the brain helping to control the feeling of irritation the allergy produces.
You can read about allergies and dermatitis in dogs here
http://www.lbah.com/allergy.htm
Dogs can develop allergies to foods, and to inhaled items, and contact allergens such as rug cleaners, cedar beds, or chemicals including lawn chemicals or even flea bites.
You might want to try a different dog food that has no ingredients the same as what you feed now. Diets of Fish and Potato, venison, or rabbit etc. where the protein source is new and there is no grains in the food can work for many dogs for example.
You might want to see if some plain Benadryl helps with the itching. A common low dose is 1mg per pound of dog every 12 hours. If you choose to use that please read here about cautions

http://www.petplace.com/drug-library/diphenhydramine-benadryl/page1.aspx

Or you may want to consult with your vet and consider doing allergy testing.

You may want to try a Chlorhexiderm shampoo from the pet supply store in case the problem is a bacterial skin infection.

This breed is also known to have low thyroid level issues and that can trigger skin allergies.
The vet can check for that with a blood test.
If your dog is not on a flea prevention that might also help. Just one flea bite can make an allergic dog itch all over.

With the eating and not gaining weight you may want to consider doing a worming with her using a broad spectrum wormer such as Panacur or the over the counter product Safe Guard.

Hope this helps you!

As worm life cycles run 2-3 weeks on up to 3 months she may need to be wormed again. Usually you worm in a series based on the life cycle of the parasites the dog has not just once.

Glad to know I'm giving you the same information as your vet for next steps. No way to know what info you have already unless you tell us and we can only answer the question you ask which was what could it be and might it be yeast.

Yes it might be yeast or staph infections from allergies thyroid problems etc.

If Chlorhexiderm does not work for a shampoo then Malaseb might. Be sure to follow directions on how long to leave the shampoo on and how frequently to wash the dog to limit infection growth.

The bad smell can go along with yeast or staph infection or a low thyroid.