The picture you posted looks like your bird is worrying with the neck wound and not letting it heal.....how dry is it in your house? I ask this because dry climates/houses can cause a bird to pick at dry, itchy skin and having been prescribed anti-itch medication, your vet is apparently thinking the itching/irritation is relevant.....
If you do have the option of taking your bird to another avian vet, at least you'd have a second opinion...if you don't have the option of another avian vet, ask your vet about an Elizabethan collar, it would prevent the bird from getting its beak on the neck wound & if properly sized, probably keep him away from under the too.....
There has been several theories, posted by different veterinarians, that while self mutilation may start with one thing, like itchy, dry skin, it quickly progresses to the bird giving itself a cheap, endorphin high, much like lids that tend to cut themselves, not to really do damage, but to get the euphoric feelings that endorphin releases create.....
Unless your bird lives in and was raised in a very dry climate, they should be in an environment of between 30% & 70% humidity and temperatures from near freezing to around 85° F.....
I think you need to, as the others have posted, seek another opinion, have an in-depth discussion about the whys of the medications he has prescribed and do a lot of reading about why birds mutilate...there are a lot of reasons and no quick solutions, but I would inquire about the possibility of a collar for your bird.....good luck.....