The single most effective thing you can do to help your paw licking dog is to use a cheap, warm steam vaporizer in the room where she sleeps. They cost $16 at any drug store.
In the summer, tree and grass pollen can make dogs skin itch. But a huge factor is dry skin caused by dry air. When air conditioners cool the air in your house they also remove moisture. The condensation that's dripping out of that little tube is coming from the air in your house. Dry air can make your dog's skin dry enough to itch. And itchy paws cause dog paw licking.
During seasonal allergy flare-ups, a steam vaporizer can often really help dog skin itching problems. A vaporizer won't solve it, but it will help.