It's not uncommon for wounds on the paws to get bigger, especially if the dog walks on hard or rough undergrounds. The protrusion is most likely the soft tissue of the paw that is infected and swollen. For a wound it doesn't look too bad and I don't expect any lasting damage once it starts healing.
As for the white mass, although the picture quality is very high, it's hard to see among the fur. It's impossible to tell what exactly it is without actually examining it, but it could be a random swelling or an encapsulated foreign object like a small stone or an awn of a seed.
You should keep an eye on it to make sure it doesn't grow or get any worse, but it seems acceptable to wait till your next vet appointment. Let the expert (the vet) examine the thing and figure out what it is.
The important question here is: Does the dog nibble at the flesh wound? If yes, he might very well be the reason why it grew. It might also be an indicator that the white mass is bothering him. By trying to eliminate this disturbance (in dog style: by licking and nibbling at it) he might have caused the flesh wound in the first place. If you notive him nibbling at his paw, put a "collar of shame" on him or bandage the paw.
In the meantime I propose buying or crafting a bandage shoe for your dog. This not only protects the wound from dirt, it also offers a soft surface to walk on.
If you decide to buy ready-made dog shoes, make sure to buy padded ones. Put a clean (read: sterialized, taken from an intact package) wound dressing from a first-aid kit into the bottom of the shoe and change it daily.
To create a makeshift dog boot, follow this instruction (just don't put laces in them) or this one. Make sure the toes and claws have ample space in the front while the dog is standing on his paw. Again, put a clean (read: sterialized, taken from an intact package) wound dressing from a first-aid kit into the bottom of the shoe and change it daily.
To further pad the shoe, you can cut a few inches of a cotton bandage and fold it to the size of the paw. Cut it to shape and fix it with tape, then put it into the bottom of the dog shoe.
A warning for everyone who didn't pay attention at first-aid curses: NEVER put paper tissues, paper towels, Kleenex, toilet paper or similar absorband papers on an open wound. They shed small fibers that can get stuck in the wound and cause complications. First aid kits contain special wound dressings that don't shed fibers and come in a sterialized packaging.