Okay So I can help you with this
I had the same thing happen a few years back. I adopted a little polish pullet. She was in bad shape. Very skinny and was infested with mites. She also had a bad ear infection. Her sinus infection was so bad that she had foam comeing out of her eyes and she wasnt even able to see. And she almost lost an eye because of it.
So the best thing you can do right this very second is go to your local feed store and buy poultry grade dust or seven dust. Powder her really good.
So she isnt eating. Check her crop. Does it have anything in it or is it empty?
I would like to point out if your bird is sick and not eating that you shouldnt feed them any sort of wierd food. Any sort of fruit or vegetable can make them get runny poo. And for sick birds that is not good.
The best thing to feed a bird when its sick is its regular food.
If her poo is runny then give her Oatmeal
And if she is not eating properly then you will have to feed her yourself.
I will tell you how and what to use.
Instead of feeding her the food dry wet the food with some water. (Using crumble food works better by the way) Enough to make it when you try to roll up small balls it doesnt crumble apart or to wet that its runny.
Added a bit of sugar. Mix it up real well. Now this is the part that isnt fun. Open the birds mouth and put a piece of food in the back of the birds mouth so that she has to swallow it. She will struggle and try to get away. Every so often you will have to give her a swallow of water so it easier to gulp the food down. Try using a syringe (without needle).
Keep going untill her Crop is of good size. Usually you can tell when a bird has had its fill.
If you want to save a bird then this is the best way to go.
The runny nose is a sign of a sinus infection. The best thing to do is keep her is a nice warm area where other birds cant bother her..
The red around the face is its natural color. If bird is sick then you won't see color.
So red is a good thing. That means she is doing good. I think its because she was living in a bad place and where she was kept was in bad condition thats why you didnt see red. So I am sure over time she will get better. Just make sure it doesnt turn into anything worse
Now the infection. Now if its something you are worried about then you can treat it yourself. All you will need is Mouthwash(the regular yellow kind, not the minty flavored stuff), water and a cotton ball.
Get a cup added warm lookey water. Added a bit of Mouthwash. Enough that you can taste it in the water. Take a cotton ball and gently dab the area with the cotton ball. Do this 2 times daily and until healed.
Betsy's Mom :
https://www.backyardchickens.com/forum/uploads/42245_dscf3546.jpg
Here is a picture of Honey. I went out to feed her a lunch treat of scrambled eggs but she wouldn't eat them. I put them under her beak and she pecked once and turned her head away. She wouldn't try the banana I brought her either. She eats her crumbles but any time her head is down to eat she sneezes and puts her head straight up and sniffles and then holds her beak open for a little while like she is trying to breath out of her mouth. She has crusty discharge on her beak which I wipe off even though she protests loudly.
I'm going to go get her the vitamins that were mentioned earlier but how do I give them to her?