You need to record an episode of the gag/cough to show your Vet......It may be simple like a
reverse sneeze, but in a dog this young, you need to make sure it's not a heart defect! Depending where you purchased this dog, I would be suspicious.....Tracheal collapse comes on with age.....Normally, not this young....
Itchy can be anything from fleas to improper diet to environment to shampoos.....It takes a process of elimination to rule them out......