Stop the bleeding: Apply gentle but firm pressure with paper towels. You can use blood stop powder if necessary. Cornstarch works also.
Asses the injuries: Check to make sure there are no other injuries on the chicken. Look under wings, part feathers and check her all over. Puncture marks can be hard to find but easily get infected, so check very well. It's easier to treat them when they're fresh then try to treat them after they've become infected.
Clean the wound: I like to rinse with saline solution to get the bulk of the dirt out of the wound. You can make your own saline solution. Make sure it's room temperature if you make it fresh. Use a large syringe (without the needle) to flush the wounds. After all the visible dirt is gone, gently pat dry and rinse with hydrogen peroxide. Allow to bubble then dry gently by dabbing with a paper towel.
Next I use Vetericyn spray to get rid of any bacteria that may remain. Then let air dry for a few minutes.
The next step depends on where the wound is and if you'll be able to cover it or not. If it's something you can wrap or cover in some way, just skip this step. If it's not something you'll be able to cover you'll want to use blu-kote on the wound. When chickens see red they peck at it and a flock can very quickly turn a small injury into a gaping hole. Blu-kote turns it purple and they suddenly have no interest in it. I know it sounds silly, but it works.
You'll want to apply antibacterial ointment next. I like to use Neosporin but any triple antibiotic ointment will work. Make sure it is NOT the kind with pain relief! That contains an additional ingredient that can be toxic to chickens.
If it is an injury you can wrap, cover it with a gauze pad and wrap with vet wrap. Be careful not to make it too tight to cut of circulation, but you do have to press the wrap together a bit to get it to stick.
I check the wound daily. If a wound gets dirt in it I rinse it with saline solution and use the Vetericyn spray again. Reapply ointment until it's healed
Depending on the extent of the injury you may want to separate the chicken from the flock. I use a cage inside the coop so she can still see her friends while recovering. I find this minimizes stress when she is allowed back in with the flock. If the injury is on her back you could put a chicken saddle on her to minimize picking and exposure to dirt.
Ideally you'll have everything you need on hand. I wrote about whats in my chicken emergency kit and it's a good idea to be prepared, but if you need to pick up a few things most feed stores carry everything you'll need.
When dealing with an injured chicken I like to add some vitamins and electrolytes to their water the first few days. Make sure she's eating well. You can add meal worms, yogurt, BOSS or cooked eggs to their food to increase the protein level and help her body heal. Most chickens bounce back quickly from minor injuries and within a few months you won't be able to tell they were injured at all!
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