Very good point that Scott has just made about taking him only to either a Certified Avian Vet (CAV), or an Avian Specialist Vet who only treats birds...A lot of people mistakenly take their parrots to an "Exotic's Vet" who treats every type of animal/pet imaginable, but has no extra education or training in treating any of them. They will see a reptile and then a dog, and then a bird, and then a rodent, etc. And birds are very, very unique in their anatomy, physiology, and most of all, in their behavior when they are sick or in pain, and there are quite a few Avian-specific conditions that a Vet will not be aware of at all unless they are an Avian Specialist...And with something like this, it's going to be extremely important that the Vet that you take your bird to knows about bird anatomy, and of any specific conditions that might cause something like this.
I've not ever seen anything like this, not ever. It's location is quite alarming, as it looks like it's actually coming out of that open depression/hole that is located under the bottom of their beaks...That area has a very large blood-supply, and is connected to both their neck/throat, their Crop, and then of course the floor of their mouth...So this could be just about anything.
Be sure that whatever Vet you do take him to doesn't just look at the bird visually and then just tells you that it's "probably due to an infection of some kind" and then just gives you an Antibiotic to give him. Unfortunately a lot of Exotic's Vets do this all the time because they don't know what else to do; they fail to run any diagnostic tests at all and just put the bird on an Antibiotic, like Baytril, and that's it.
I can't tell just by looking at the photo whether that is actually a "growth", or if it's simply the bird's own skin/tissue that is just badly swollen; I also can't tell if it's hard, soft, fluid-filled, air-filled, etc. These are all things that the Vet needs to determine by doing some diagnostic tests, and that's what I mean by not just allowing the Vet to look at your bird and then just prescribe an Antibiotic and maybe also an Anti-inflammatory and that's it, without doing any diagnostic testing. Depending on what it feels like and whether or not it's an actual growth or just the bird's skin/tissue swelled-up, the Vet should either do a Fine-Needle Aspiration, where they take a needle on a syringe and try to draw fluid from the mass/abscess, or if it's a solid growth they need to take a Fine-Needle Biopsy and send the sample off to a lab for diagnosis. I wouldn't be at all surprised and would even request that the Vet also take a regular X-Ray so that they can see how complicated and involved it is, and then would also probably request that they draw some blood and run routine blood-work at the lab to rule-out an infection, among other things. They need to actually make an effort to properly diagnose exactly what this is instead of just guessing and just "seeing" if antibiotics and/or an anti-inflammatory will make it go away...This could be nothing or it could be extremely serious...
Again, it's very rare that an actual Tumor or Cyst would just suddenly appear overnight, or even in a matter of days. An Abscess might form very quickly, but there should be other signs of infection or the cause of the infection, such as an open wound, a bite, discharge or bleeding from the bird's mouth/throat, etc.
*****I forgot to ask you how your bird is acting otherwise...Is he behaving normally? Eating and drinking normally? Has he lost any weight? Are his droppings normal, or are they watery/runny? Any blood in his droppings, or any bleeding from his mouth, nostrils, or anywhere else? Is he acting lethargic or sleeping more than usual? Any vomiting? These are the signs/symptoms that you need to be looking for so that you can tell the Vet about them as well...
