You can buy saline at most pharmacies. If you want to make your own you can add 1 tsp of table salt to quart of water, bring it to a boil, and reduce to simmer for 15 mintutes covered to sterilize it. Store it in a quart canning jar.
Vetericyn wound spray from feed stores is a very good thing to use. Plain triple antibiotic, neosporin, or polysporin are all good for deep or puncture wounds and used twice a day. Peroxide won’t kill her used once, but they have found it may prevent wound healing.
Antibiotics may not be needed if wounds are treated daily. In fact most are not approved for poultry in the US presently. In the future, Hibiclens (chlorhexidene) with water is a good disinfectant wound wash for cleaning initially. It is used in hospitals and for surgery. Be aware that green skin may be a sign of bruising. Trimming away feathers that get into the wound may be helpful.
I had hen who had similar injuries, and she could barely stand on day two. She made a full recovery and resumed laying a few months later, although her eggs were thin shelled from then on.
I would treat her every day, and think about letting her spend some time in a dog crate with food and water in the coop once or twice a day if possible. Her deep cut should fill in nicely without stitching. There are plenty of threads of wound healing if you use the search forums above. Good luck.