Why is my dog's nose sore getting bigger and he keeps licking it?

Depending on your dog's age and clinical signs, this could be a few different things. A fungal infection is certainly possible, and if this is the case, it will definitely require a systemic anti-fungal rather than something topical to rid the problem. Bacterial or viral infections can also cause this sort of thing. Another distinct possibility are certain types of tumors. One that come to mind in particular is call a TVT (transmissible venereal tumor). We see this a lot in young, in tact male dogs although it can in theory occur in any canine. Other cancerous growths can occur on the nose and face as well, but this one is fairly common. The only way to know for sure will be to obtain cytology and/or biopsies of the affected areas. I would strongly recommend getting Vador into the vet to be examined sometime soon. These sorts of things are best dealt with head on in the beginning. Hope this helps.