My hubby (Army Veteran of Desert Storm) and I hike/camp, so we have quite the first aid kit, varied sizes of sterile gauze, steri-strips, butterfly band-aids, assorted bandaids, kerlix rolls, hemostats, tweezers/forceps, ACE wraps, finger splints, various tapes, scissors, sterile and non-sterile cotton swabs, betadine, alcohol wipes, varied antibiotic ointments, silvadene cream, superglue (works quite well in place of dermabond in a pinch, and is MUCH cheaper), epi-pens (we have 3 beehives, so we keep them on hand, just in case), "break open" hot and cold packs, Vetrap (self adherent bandage) works great for pressure bandages, various size safety pins, razor blades, possibly a scalpel or two, penlight, stethoscope/BP cuff, tourniquets. I stock/rotate out a varied supply of benadryl, baby aspirin, tylenol and motrin, and sterile saline eye drop individual packets and hand sanitizer and liquid soap (these work in a pinch to irrigate any wound).Bottled water and hand sanitizer and liquid soap.
I think there are a few OB tampons (regular), as those can be used to stop a gushing nosebleed until able to get to an ER, (tape string to side of face).
We also have water purifier tablets in there as well as candles with waterproof matches and a zippo lighter. I am sure there are other things in it, as I haven't checked it recently. Between his combat experiences and my having worked ER, we both know first aid quite well.
I know how to splint a fracture well enough, until one can get to an ER for further evaluation.
(I have 3 sons, all were very active little boys and I learned quickly what we needed to go to ER for and what I could manage at home with a little ingenuity!)