if the nose rope isn't clearing up with the anti-fungal cream, like @bullmama said it's probably bacterial.
the throwing up is odd, but i don't think it's related to a protein allergy or he'd be throwing up all the time. i'd probably take him to a vet at this point so they can do a culture on the nose rope and give you the correct meds. would also mention the vomiting.
if you can, maybe put him on a bland diet of boiled chicken or hamburger with rice to settle his stomach, and then slowly incorporate a new kibble after he's able to hold everything down for awhile.