Hello & welcome, I am Dr. B, a licensed veterinarian and I would like to help you with your wee ones today.
First, I have to say that I am quite worried about this lass.
Open mouth breathing in birds is a sign of respiratory distress and often an advanced sign that can be seen with respiratory disease. And if she is struggling to breath so severely, it is not surprising that she cannot eat/drink since she likely hasn't a breath to spare. So, we need to tread with care here and be proactive.
Now as I am sure you can appreciate upper airway signs like these can be seen with a number of respiratory agents. Therefore, we have a lot of agents to consider here. Specific concerns include Infectious Coryza, Acute Fowl Cholera (Pasteurella multocida), Influenza, ILT IRT, infectious bronchitis, Chlamydiosis, and mycoplasma (Mycoplasma gallisepticum). Furthermore, since you noted that one bird is gasping (which can mean there is swelling, discharge, possibly infectious material or worms blocking up the throat) we can see localized throat based disease due to Trichomoniasis (canker), Fowl pox (wet form causes canker lesions in the throat) and Syngamus trachea (gape worm) infestations. Most of these will also cause the eye signs you have reported, though secondary bacterial conjunctivitis often will appear in these situations when the immune system is under attack.
Now any respiratory infection of the bird must be taken seriously since respiration is critical to life. If you are comfortable handling this poorly bird (and she doesn’t get to distressed with this), then you can potentially narrow down a few of these differentials at home. If you are comfortable doing so, you may consider having a peek down her throat to rule out you gapeworms. You may be lucky and see them or one of the other causative agents (ie the plaques of Fowl Pox or discharge of canker). If you can't see anything, since you can only look down a chicken throat so far, then you can try the "Q-tip test". To do this, you need to place the bird in your lap, gently open her beak, and swab a cotton bud down her throat (twirl it as you do this). Twirl as you bring it back up, and if she's got gapeworm, you'll see thin, red strings on the cotton bud. This way you will know if this is the cause. But if you end up with a cheesy discharge then canker or pox would be higher on the differential list. And if there is any other discharge, the bacterial causes would be suspect. And once you have identified what is present, you will be in a better position to treat her.
Otherwise, further measures to pinpoint the causative agent and increase your treatment success, you do want to consider involving your vet. Especially as a gaping/gasping bird that is showing very advanced stages of disease likely needs intensive care +/- oxygen if she is going to survive this. Therefore, you'd want to have her examined by your vet. They can listen to her lungs, examine her airway, and help you determine the disease local and therefore rule out some of these agents. Furthermore together you can collect some respiratory secretions from this bird to be cultured. This will tell you what agents are present and what treatment will actually clear them . As well, you might consider having a fecal exam performed as well to tell you if parasites are playing a role (directly or via compromising the immune system).
Further to this, once you have samples for culture (which will tell you what drugs any pathogenic bacteria present are vulnerable to), you can consider a broad spectrum treatment to try and tackle as many of the bacterial causes as possible. There are a range of options that would include erythromycin, oxytetracycline, or fluoroquinolones (useful if Mycoplasma is diagnosed), macrolides. Other options may be tilmicosin, tylosin, or spiramycin.
Otherwise, supportive care is that key facet that we need to make sure you are addressing for her. If you have not already, she should be isolated from the others to prevent spread of infection. If her eyes are very mucoid, you can flush them with sterile saline (ie OTC first aid eye wash, plain contact lens solution) as needed. As well, if she sounds very congested (if not suffering form an inflamed airway), you can try to reduce her congestion by using a bit of steam treatment here. You can achieve this by putting her in a carrier in the bathroom while you run a hot shower. Or if you have a nebulizer/humidifier you can set up a wee steam tent (by putting her into a carrier and covering it and the humidifier with a bed sheet). This can just help reduce some of those airway clogging secretions and help her to breathe easier.
Overall, there are a range of agents that can be to blame for the signs you are seeing with the gasping lass. Therefore,since she is in an advanced severe state ,you need to initiate the above supportive care, monitor breathing, and take some of the above diagnostic steps to determine which is to blame for her signs. If you narrow down the differentials but cannot identify a cause (ie if its one of those more subtle ones or is lurking in the lungs), then it would be ideal to follow up with your vet urgently to give her a chance. Especially because your vet will help you treat but also identify the agent present. And that will let you ensure you are treating as effectively and economically as possible to make sure you are able to limit the disease's effects on her and prevent spread to any other birds.
If you have any other questions, please ask me – I’ll be happy to respond. Please remember to rate my service once you have all the information you need. Thank you and hope to see you again soon! : )