These are likely symptoms of an upper-respiratory infection -possibly choryza or sinusitis- a combination of both- or just the underlying mycoplasma infection that serves as the underlying infection from which those two more nasty bugs sprout. Ypung chicks inhale fines from chick starter, together with feather dander, atmospheric dust and fecal material- some of this they preen from their feathers, rub into their eyes and nares and so on. Boost their immune systems with a few pomegranets and pieces of frozen prawns/shrimp cut up with the shell. Also, load them up on nuts and get them into a dog crate perched up high in a room where if/when they escape from that carrier they will not be able to escape further- you'll only want to treat them -with bird in hand at night- never during the day-
All of this is in preparation for post treatment-where they'll be outside. That outside enclosure should not be stressful so make sure that the enclosure has plenty of dried leaves and or straw- not hay- straw on the ground with plenty of sheltering boards-lean them - give the birds something to hide under. If they are more stressed when moved out they'll not kick the sniffles- it could get worse. I've been working with birds as an avian vet tech for more than twenty years. Please heed my advice.
Don't start with antibiotics until you get their immune systems kick started. Antibiotics kill good bacteria along with bad bacteria. So first and foremost help the birds's natural immune system to get to work.
Next- after the birds have had their immune systems bumped, in their tony new digs in the dog carrier- for a few days- be prepared to treat for an upper respiratory system infection- in a few days. This is going to require an injection of contact lense solution- the three and one type that cleanes, rinses and stores - it removes protein deposits off of contact lenses- it rinses the lense if you needed to pour it directly into the eye and it can be used to store the contact lense over night. Make sure it does all three of these things. Baytril injectable -just a tiny drop is all you need mixed into a quarter cc of contact lense solution. You'll be injecting this directly into the sinus cavity. Injecting a bird with antibiotics into the breast is not as effective and harder on the bird. The entire bird is not infected, its nasal passages are. The fines it inhaled as a young chick are lodged throughout its air sacs and these have no blood running through them. Then the birds inhaled the dust of the chick brooder room- with its feather dander, fecal material, atmospheric dust and more fines from chick mash. These have become lodged in the sinus cavity and are coating the birds' plumage every time they preen- rubbing more into the nares and eyes.
Injecting the material between eye and nostril is scary but if you are going to be rearing birds its something you will have to learn to do. If you have some rug rat chickens running about- practice on them- with just saline solution. This will help you get confident. If you have any dead birds in the freezer with their heads still attached- better yet- but most people will not have a dead whole bird in the freezer. Regardless- get ready to do this in a few days after the immune system has been given an opportunity to recalibrate. When injecting this solution into the nasal cavity, liquid is going to pool from the eye and from the nostrils- it will also come out of the bill- this is what is needed for it to reach all the right places. Treat both sinus cavities even if only one side appears swollen- if it's gotten to that stage.
It's hard to remember but Chrysolophus pheasants are semi-migratory in nature. They ascend in spring and descend in autumn. Their plumage colours enable them to forage for food larders in the foliage as it changes colours. This is critical as winters are particularly taxing in their native ranges. They will be gorging on berries of brambles and rosehips, cottoneaster, partridge berry and so on- during the fall. These are loaded in vitamins and fibre, antioxidants and so on. The pomegranet is available for very little this time of the year. Crack one open. Let them eat the entire fruit. Feed them walnuts and hazelberries if you can find them- shelled obviously- and moisten their daily maintenance ration with sesame oil- preferably the kind with chile oil in it- yes it's very spicy. These easily procured ingredients will fill the crop- the oil lining the esophagus- seeds will cram into the gizzard- the entire digestive system should be filled to some extent- a bit like a toothpaste roll- you want them to have loads of super nutrition throughout their system before you begin treating them with highly invasive and toxic antibiotics.
Once you do start them on an antibiotic mix plain yogurt to the walnuts and other nut meats for at least one week.