First to better help us help you (accurately) could you please possibly answer the questions from the sticky post listed below - but answer into this thread so we can read it? That will give us a better idea of the environment as some respiratory illnesses are fungal/environmental, or ammonia caused, and the other info will help us with the illnesses that aren't of that type.
The sticky post:
https://www.backyardchickens.com/forum/viewtopic.php?id=3569
To that I'd add these questions: If you open her mouth and look inside, do you see any nodules, anything cheese at all at the roof of her mouth?
Many very common respiratory illnesses are indeed bacterial primarily (MS, MG, cholera/pasteurella, bacterial pneumonia, coryza, etc), and viral respiratory illnesses often have secondary bacterial consequences (IB, ILT, END, etc). Of course, the ideal situation is that you would take the bird to an avian vet (or any vet), have them swab the secretions and the choana (cleft in the roof of the mouth), listen to the lungs, and grow out the culture into a "culture and sensitivity" to tell you exactly what the name of the bacteria is (if there is one), and exactly what medicines to use.
In the mean time, if you choose to treat on your own there's a bit of guesswork that goes on with that and it's never guaranteed. Please do know that.
With your bird, because of the coughing and bleeting, I would be concerned about a lower respiratory issue (of any origin - bacterial or fungal or viral) as well as an upper respiratory issue (sneezing though no nasal discharge, etc). Also because of that, I'm concerned about it being infectious bronchitis (viral) which doesn't have a treatment per say.
I also think that her being broody is part of it as this is about 2 weeks in duration. Is the coop dusty at all? Does it have excellent ventilation? Any chance of dust mites?
For all illnesses, there is a set of supportive care that helps the bird to heal. With any question of respiratory illness, I like to hit it from all angles: Nutritional, probiotic, medicinal (if applicable), environmental, and supportive treatments. Here's what I do and recommend based on my success and what I've researched about each part.
First, nutritional: for any respiratory illness or irritation, vitamin A is a good vitamin to use (with care - it's an oil vitamin so you don't want to over load it). This doesn't sound like a vitamin deficiency as there is a lack of clear discharge from the eyes, cheesiness there, etc. (The throat question will help rule that out.) That being said vitamin A is still very important for respiratory healing and a little boost will do nothing but good. Because she's not apparently deficient, I'd recommend something like a good balanced poultry vitamin/mineral supplement like Aviacharge in the water. Alternately, I really like using Enfamil's PolyViSol vitamins as they contain a nice vitamin A and if you give 3 drops in the beak daily for a week, you don't have to worry about light degrading the vitamin A before she gets it. There are other vitamins as well (D, E, B, etc) within a nice range.
Make sure the bird is getting 95% of their diet is a completely fortified age-appropriate feed (pellets or crumbles). If pellets and the bird is reluctant to eat, I break them into crumbles in my blender. If they're still reluctant, I offer some damp (not wet) mashes. More on that below. It's important that the bird get a richness of nutrition, balanced for poultry, especially when any questionable health issues or symptoms come up.
Make sure the bird is eating and drinking. Sick birds (like people) often don't feel like eating and drinking. We must facilitate both. Be particularly careful, however, about giving them water as they are less able to swallow carefully with mucus in their throats. You don't want to aspirate them. I never recommending pouring anything into a chicken's throat or back of its beak. If I give anything, it's in drops or small a mounts of paste that can be tongued back safely past the airways.
Just know that as poultry stewards we're responsible for making sure they still eat and drink during illness. If a bird won't drink much, using an electrolyte solution (for poultry - as labeled) helps tremendously. Do not mix with meds.
For illnesses not including protazoa (coccidiosis, etc) then you can consider adding some extra protein for healing. Boiled/mashed eggs are great for this - especially in hiding some of the healthy things you will want to add, like the vitamins and probiotics. As with all things, don't overdo it. Use it to your advantage however.
Probiotics: Any time there is stress, illness, and particular with respiratory situations (because any interior drainage will drain through the roof of the mouth from the eyes/nose into the digestive tract) I recommend using probiotics. PRObiotics are non-medicinal live bacteria that bolster the number of already existant live bacteria upon which the digestive tract depends. Sinus drainage, stress, etc can decrease the number and quality of good bacteria - leaving the digestive tract more susceptible to opportunistic bacterial and fungal infections. So I give more live bacteria of the type that actually colonize the gut: lactobacilli . If you're not treating with a med that ends in -mycin or -cycline (see the label of anything you use) then you can use something as simple and cheap as plain yogurt. It has live lactobacilli in it, is tastey to most birds, and is readily available even in the middle of the night. If you use one of the above mentioned meds, then use either acidophilis capsules (for humans, vitamin section of the drug store,
walmart, many grocers) or a prepared live-bacteria probiotic like Probios. (read the label - it must say something about CFU numbers to contain live bacteria.) The powders require less bulk and can easily be hidden in some yolk of a boiled egg mixed with water. The birds won't even know they're being tricked into a healthy treat.
Supportive treatments: These are non-medicinal but really help. I really do like using VetRx for any birds with congestion, sneezes, anything upper or lower respiratory. VetRx (of any variety) is available at many feedstores and often at
TSC (call first). It is an herbal fuming remedy like a chicken-safe Vicks (Do NOT sub vicks). Its use is that it helps open airways and help with congestion and mucus so that the birds breathes better. Birds that are more comfortable heal better. Birds that can't breathe do not eat or drink; birds that don't eat or drink don't heal. I mix equal hot water and VetRx in a cup. I mix that with a q-tip. One end of the q-tip for each spot, a new q-tip for each bird. Use the mixture to swab each nostril clean, to swab the choana (cleft opening in the roof of the mouth) to send fumes into the sinuses and into the lungs. Swab under the eyes near the tear ducts (not in them) and even where the bird puts his head at night to sleep. One small 2 ounce bottle (around 6 dollars) lasts a very long time used this way. If you can't find VetRx, big chain petstores may carry Marshall Pets Peter Rabbit Rx (pronounced 'rix'). It's the same formulation - use it the same way.
Environmental: make sure the bird has lots of good ventilation - never stagnant air, particularly during illness or suspected possible illness. Well always really. Sunlight is a brilliant disinfectant and is very healthful to birds (within extremes). If you can get them in some light with some fresh air, they will do better. Feel better = heal better. Make sure their bedding is less dusty than usual but very absorbant and dry. Keep them a little more warm than usual if it's cold outside, but of course keep them at a good safe temp in warm times such as this time of year.
Check particularly for any mildew as birds will be more sensitive to mildew and fungi and fumes during periods of respiratory problems.
Other: Be sure to always take care of your sick bird last. Using a man's shirt or something that you put over your clothes helps lessen the spread of disease. We use anti-bacterial alcohol gel on our hands leaving the sick bird (so we don't contaminate doorknobs) and then wash our hands inside. Separate the bird into a place where they can readily access feed and water.
In your case, I'd do all the support of a respiratory illness as that will really help all healing. Then I'd try to determine if it's a lower respiratory bacterial problem (even if secondary) and if so, treat correctly. Unlike most respiratory illnesses, a lower respiratory illness sometimes responds to penicillin. This is a hard call as we're not vets, and there's not a vet to make a culture. But definitely put your ear against her and figure out where in her body the congestion is. If you can tell us that, we can help you figure out what to do about treating.
In all cases, please let us know what happens with this girl. We're very sorry she's ill, and some of us are subscribed and will be waiting for your reply . It may be something viral, but congestion like that concerns me so any changes are important.
This is a LOT of information. Please feel free to ask here, PM, or email if you have any questions on the above personal recommendations. Thank you!