I would also include to the list Mizzely posted...
I also keep Liquid Band-Aid on hand. I use Band-Aid Brand as it has little smell. NO, THIS IS NOT THE BEST THING FOR A BIRD TO SMELL OR CHEW, but when your bird is in an emergency situation with bleeding, it does work and may be the difference between life and death.... just in case styptic powder and cornstarch don't work...
Heat Pad or Lamp Heat is very medicinal to birds, and a sick bird may not be able to maintain his body temperature until you can reach medical care. Ideally, some tub or small cage works best. Be sure the bird still has access to food and water easily. MONITOR how you provide heat so that you do not overheat your bird.
IODINE and/or BETADINE should be included to sanitize a wound.
You might think this next item is overkill, but I, unfortunately, learned the hardway...
My BIRD SAFE "MEDICAL" CARRIER is brand new and never used... it "sanitized" by comparison to their regular carriers and it is ready to go... I have clean towels and a heating pad that can be plugged into the car's cigarette lighter already set up in the carrier...
2 Avian Vet’s Phone Numbers and Addresses are written in indelible black ink the top of the carrier just in case something happens when I am not around, so people know who to contact and where to go without wasting precious time trying to track me down or figure it out.... my vets have my CC info on file God Forbid they need it!
BE PREPARED: emergencies with our pets happen when we least expects it!