His eyes don't look swollen to me in the photos. It looks like he's in a ton of pain, and birds tend to shut their eyes when overwhelmed like that.
That's a lot of blood around his mouth! Is it all his? Do you know the source of blood around his beak? Hopefully it's possum blood...?
Birds can shock easily (also might be why his eyes are closed). If it were my rooster, I'd keep him dark, quiet, and disturbed as little as possible. I wouldn't put him on prescription antibiotics unless I confirmed an infection, as it will reduce his immune system needlessly otherwise. Not a personal fan of "preventative antibiotics" or "just in case". Infections aren't usually a death sentence, they are a natural part of the healing process and can be easily treated and managed as needed.
That said- immune support, immune support, immune support. Stress is hard on birds. Good calories, good probiotics, good electrolytes. Reducing bodily stress; keep him warm, clean, and immobile. I would trim his feathers with scissors anywhere and everywhere til I found his wounds. I would flush and clean any wounds I found with vinegar water and trim all feathers away from any torn skin. Any major tears scan be stitched shut with needle and threat if need be. Bird heal wounds extremely quickly, so sterilizing any punctures before they seal over would be my priority. If already crusted over, I would soften in warm salt water and re-open the punctures so they can heal from the bottom up.