This topic came up one time on YorkieTalk and someone shared this site.
Dog Paw Licking and what you can do about it
I had no idea there were so many reasons for pawlicking. But, it does sound like allergies are the most common.
For my Piccolo, she licked her paws for 2 months and I could not get her to stop. I took her to the vet many times. What I did not know until later was that this was a symptom of cutaneous vasculitis. I did want to add that this is not a common reason , but just another example of one of many reasons why our pets might do this.
Hope you get things figured out quickly.