The really devastating thing about these diseases is that a lot of them can't ever be cured once the birds have them. You can treat the symptoms but they will reappear every time the bird is stressed, such as coming into lay, during a molt, during a cold snap, etc.
You can try to treat this and it will get rid of the symptoms but the birds will possibly carry the disease for life and if you ever do get more birds they will pass this on to them. If there is a bad smell coming from them, especially from their nasal discharge, it's likely coryza. If no smell, you can try treating for mycoplasma as it is possibly that. To find out definitively what it is you could ask a vet to run a blood test (which will probably be expensive and upwards of $100) or you could cull one and send it for necropsy. These are the only ways you will ever know for sure what this is though, and you have to be aware your birds will quite possibly be sick for life even if you do treat them now.
There are a couple viral diseases it could be too, such as infectious bronchitis, and that would just have to run its course on its own and treating won't help, but again, to find out what it is you'd have to test or cull one and send it for a necropsy if you want to be sure.