It can be any one of those illnesses, symptoms mimic eachother.
Usually States have a laboratory that do testing at no charge because they are also set up to monitor large, commercial poultry organizations.
Regardless of where you get testing, small vet or the State lab, IF the results are of ANY illness or disease deemed contagious, it will be reported to the State, as that is the legal protocol.
When it is a large commercial poultry business, they actually must provide samples ongoing, of their flocks, because chickens are coming & going constantly. When they get a contagious disease, it can be overwhelming & devastating. Years ago there was a viral outbreak & many poultry businesses had to euthanize hundreds of thousands, it was just horrible from what I've heard.
Yours is probably a small, private back yard flock, no birds coming & going. What they are concerned about & trying to prevent is spread of disease to other flocks and other chickens elsewhere & safety to the general public. That's why there are strict rules and regulations about quarantines.
My friend went through this with her small backyard flock, it was MG. She had no idea, it was all very shocking, but all in all, she only lost 3 birds, that was 2 years ago. Every state is different so I can't say what another state will do, but at least in her case, they were lenient in letting her try to make her birds well, and gave her a few months to try several medications & inoculate, after they knew it was MG. When she saw medicines were not helping, she said the mucus in nares, eyes & cleft just get worse, & poor birds were suffering, she went ahead & had those 3 humanely euthanized by the Lab guy at the State facility. She told me he was very kind about it & he said it would be quick & painless as possible. She remembers a lady from the State office calling her when she was trying the different medicines, about every 2 weeks, just to see how the birds were & how things were going, what meds she tried, and they were very compassionate and caring because they knew these were her pets.
I asked her about the symptoms.
1st bird sounded congested in chest so she brought him in & put on penicillin. He seemed to improve, 1 week later no chest congestion but then his eye started to swell & nares were congested.
2 hens started to show symptoms so they were brought in, set up in their own cage. They had a bit of chest rattle congestion.
The Roo steadily got worse, bad breath, gunk in cleft, nares full of mucus, eyes got worse with swelling & mucus. The hens inside of their beaks were cheesy & stinky. They didn't have bad swollen eyes like the Roo but they never got better & had off and on chest rattles. She said when the poor Roo was getting worse and worse, she knew the hens were just a step behind, they'd end up getting worse, too. So at least she had the diagnosis to know they were not going to get well, even after trying various medications for several months. Usually, birds do not last that long with MG.
Anyway I'm just sharing this with you because I know how frightening this can be, especially if you don't know exactly what you are dealing with. Correct diagnosis would be very beneficial, so you could treat with the proper medicine. I realize you may not be able to get testing where you are. I guess we are a little more fortunate in this region because we have a lot of chicken industry nearby, so we have the resources to get testing done. As far as any kind of veterinary treatment though, we do Not have that, so while we can get a diagnosis we are often on our own as far as treatments & determining what medicines are best to treat with. I'm just sharing this all with you to try to help, and I truly hope that your birds only have canker. MG produces really foul breath but canker can give stinky breath as well. Nasty sinus infections can really stink badly too. I wish you the best and I hope everything goes well For you and your feathered friends.