I am sorry you are going through this and you are very right to be concerned, as this is very serious.
The first thing you need to do is either take your bird back to the breeder or find a genuine, avian certified vet (exotics vets and general vets are not the same, and have nowhere near the knowledge needed to care for parrots--some exotics vets acquire knowledge from experience, but with a baby in this state, it should be a CAV if at all possible).
Never buy an unweaned baby (there is no reason to-- your bond will not be stronger in the long run-- it is just encouraged by some breeders because it SEEMS like the bond is better short-term and saves them a ton of work). They all are sweet and squishy as babies, but at puberty, they often push away from the very person who weaned them anyway (breeders often do not mention that part).
Are you using PTFE/PFOA/PFCs/Teflon/non-stick (unverified source) in your home? these can be in drip trays, pans, blow dryers, air fryers, straighteners, space heaters, electric skillets, irons, ironing board covers, HEAT LAMPS (depending on the type) etc etc etc. These silently off-gassing chemicals impact birds far more than almost anything else in a home and they can kill them in as little as 5 min, but can also lead to serious respiratory distress and damage long-term when the bird survives (which, from experience, can be minutes, to years--- it's all very dangerous and has a long-term impact). They frequently kill on separate floors, with fans and windows open and through closed doors. People think they can still use them if they air the place out but that is very incorrect. We had a budgie when I was a kid and did terribly unsafe things without knowing what we were doing. Birds hide illness, so obviously, by the time they show signs, it is nearly always serious.
Products deadly to parrots are EXTREMELY common-- you are not to blame if you didn't know-- SO MUCH of what most people use in their homes (cleaners, candles, fresheners, teflon, burned food, smoke etc= very very damaging to birds).
Then there are chemicals like air fresheners, scented products, glade plug-ins, vaping, smoking, overheated oils, incense etc that are horribly bad and can permanently damage the air sacks (irreversibly).
Yeast, parasites, bacterial infections etc can all also prove extremely dangerous for babies or adult birds (hand feeding requires sterile conditions, a very strong knowledge of where to put the syringe, EXACT temperatures etc-- this is way more work than it seems). Humans should also never let a parrot lick, kiss, or contact saliva or lips in general (you should not eat or drink out of something and then allow the bird a bite). Humans and most mammals (including dogs and cats) carry gram-negative bacteria and the introduction of such bacteria (via touch, ingestion or cut can prove very dangerous). This is why hands must be so clean etc. Esp with babies.
They hide illness until things get dangerous and a bird should not be sneezing with discharge without a very immediate vet visit---especially so young.
Please, If at all possible, please just get this baby to an avian vet asap.
