My dog used to get the same thing, although she did not lick as much as yours is I dont think. I used to wipe her feet down after a walk to remove any pollen.
Best Answer chosen by Bondi Vet
Billy is certainly not alone - many dogs suffer from chronically itchy feet!
The tricky part is in determining the cause of itchy feet. Often there will an infection of either bacteria, fungus or both. These little nasties tend to make the itch and the compulsion to lick, worse. Unfortunately licking keeps the area moist and surface bugs thrive in a warm moist environment (like between the toes!). So the cycles goes on... Some dogs have an underlying allergic component to the problem and the infection comes later. Allergies can be to grasses and plants that the feet come into contact with (eg. wandering jew) or due to inhaled irritants called allergens.
A consultation with your veterinarian is the best place to start. They may perform some tests to help determine the nature of any infection present and then prescribe the appropriate medications to clear the infection and control the itch.
Skin disease can be very frustrating for owners so I know how you feel! There is no simple solution and diagnosis is often a process of elimination which can take some time. However, if you're patient and methodical, follow your vet's instructions and remember that many skin conditions require ongoing management to be controlled, I have no doubt that Billy's obsessive licking will be sorted out in no time!