Make sure to have bandages of all sizes in your emergency kit. Use the small bandages for slivers or scrapes and the bigger bandages for larger wounds. Make sure to have a roll of adhesive tape to use for gauze bandages. Put some antiseptic and/or hydrogen peroxide in with your bandages, too, to help clean out any deep and dirty wounds. Make sure to include ace bandages in case of sprains.
Keep some burn salve handy in the kit and maybe some aloe as well. Where there is a campground, there is a campfire. Kids have a tendency to play in the fire and accidents even happen with adults.
Bug repellents are a must when camping. Get a bug repellent that works for ticks as well as mosquitoes. Keep a pair of tweezers in your kit in case a tick does embed itself into someone, since tweezers make it easy to remove it. Have a bee-sting kit handy at all times just in case someone in your party is unaware if they are allergic to bee stings, which can be very dangerous and even deadly for some people.
Keep one pair of latex gloves in your emergency kit. You never know when a stranger might need your help or when someone in your own party might bleed a lot and you may not want to touch the blood. Keeping rubber gloves on hand helps to prevent the spread of possible diseases from one person to another and also helps to prevent you from getting germs into a wound causing an infection.
Pack a thermometer. You do not need a fancy one--a regular thermometer will do. This is especially helpful if someone does get an infection, you can tell if they have a fever as well, which may be a sign that you should get them some professional help. Make sure to clean off the thermometer for your next camping trip if you do use it.
Prepare for snakebites with a snakebite kit. It is a good idea to have one of these no matter where you go. It might also be helpful to get some pictures of snakes in the area where you are camping, especially if there are any poisonous snakes.
Keep some aspirin or ibuprofen in your emergency kit. This is good to have on hand in case of a simple headache, muscle aches from hiking or for fever reducing in case of some kind of infection. Keep small packages in the emergency kit and check them before each camping trip to make sure they are not expired.