Go with your ABCs, which is what's told to all first responders. A-irway, B-reathing, and C-irculation. Bleeding may be the most common threat to life with a gunshot wound, but you have no way of knowing what emergency situation life is going to throw at you. Get trained in CPR. It's changed some, so if you haven't had it recently, it might be a good idea to get the training again. In many cases you encounter, simply changing the position of the victim can open a blocked airway. Keep in mind that you aren't trying to be a medical worker. Your task will simply be to preserve life until you can pass the patient off to a higher level of care. That helps keep you focused on the things that matter most, and helps prevent you from being tied down with issues that aren't life threatening, or are of a lower priority than others. If you're going to carry tourniquets, know how to use them. Let me clarify that. If you're going to carry tourniquets, KNOW HOW TO USE THEM. Tourniquet technology has improved dramatically over the past few decades, but it's all a complete waste if you don't know how to use them properly. Worship at the altar of YouTube. Since many of the best tourniquets come in sealed packages that shouldn't be opened until use, YouTube becomes an invaluable training resource on how to use them. If you're serious about them, I very highly recommend the Combat Application Tourniquet (C-A-T) made by Composite Resources. Since there has been an issue with people making cheap knockoffs and counterfeit C-A-Ts, I suggest buying them directly from North American Rescue, which is one of the five authorized distributors.
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As Chen stated, I don't suggest using artificial clotting agents unless you're at the point where other methods of bleeding control are nonviable. However, the use of clotting agents isn't a black and white issue at all. For instance the resistance to Quik Clot among Chrisdrummer's EMT/ER friends probably stems from before Quik Clot switched to using kaolin as the active ingredient. Prior to that, some patients would have allergic reactions to chitosan, the prior ingredient made from shellfish, and there was also a significant amount of heat generated, even to the point of causing burns at times. The latest formulation generates a small amount of heat, but not enough to cause any burns. The other aggravation ER personnel had with clotting agents was in attempting to clean them out of a wound. They solidify pretty good. But that objection was based on people using it when it wasn't needed, such as a guy who sealed up a cut on his hand so he could keep fishing for a few more hours instead of going in and getting stitches like he should have. ER personnel won't complain if it's used in a true life or death situation. Additionally, it comes in bandage form now, so many of these people who used to pour it into non-life threatening cuts probably won't be doing that as often. That'll make ERs happy. However, the really big, life-threatening bleeds may necessitate the use of the granulated versions that you can pour into a wound. By the way, you may also see it as CELOX, ChitoFlex, HemCon or other such names. Anyway, points to ponder.
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Essentially, get CPR training and have a kit that addresses basic first aid needs, but that also gives you the ability to control traumatic bleeding, and that should cover the bases that have been discussed here. You probably don't want to do what I did. I have three full trauma bags. But that's because I'm an EMR and I support large events that are held way out in the boonies. Or at least I did before I broke my back anyway. The downside to that is those bags are expensive, and much of the stuff in them expires and has to be replaced at regular intervals. That's something you should also keep in mind for your personal first aid kits. Some of the contents do expire, and that's part of the reason why you may not see items in some kits that you feel should be in there. Nobody who sells those kits wants to be blamed if something goes wrong in an emergency, and someone thinks it's because something in that kit expired eight years ago.