@SinseaChicken. I asked if she was the only hen injured because this is my thinking.
Perhaps the dog sticking it head in the door made you take notice of your chickens.
I think she’s had this problem for awhile. I don’t know if you even have availablity to get Tylan 50 let alone inject her.
I go with common easy to find items (drug store or pharmacy) because a lot of people don’t stock first aid items and in a panic simple is sometimes better for those folks.
If your not used to treating your birds. Get someone to help hold her. Cleaning the eyes could be as easy as poring the fluids over the eye and let it flush out. I like to use a big soft ball of gauze to dab it. Be gentle. Repeat as needed until you get it clean.
Baytril I keep on hand mostly for my dogs. Here again easy to find. I get the 25 milligrams (lowest dose they make). It would be great if you could weight your hen but if not give her 1/2 tab up to twice a day. Put it in a grape or a kernel of canned corn or wrapped in bread. What ever she likes. This won’t help with the infection but it will help dry out her sinus and help with swelling. And make her rest (makes them a bit sleepy for awhile)
It’d be great if you could bring her in or at least in a crate or her own separate area of the coop. Even a box.
I don’t know what your comfort level is in handling your chickens. I don’t know what you have on hand. Best wishes