J is for Just a Flesh Wound

'Anyone who has been shot in the leg and tried to walk immediately afterward was not hired as the technical consultant on this movie.'
—Roger Ebert, reviewing Gunmen

My best friend from high school is an emergency first responder (ie firefighter and paramedic) in a remote area of Texas. Besides the high number of calls to rescue drunks who have been bitten while goading rattlesnakes, she sees a large number of people who call for help pretty late in the game, mostly because they underestimated an injury.

In Fictionland, any injury that is not a direct hit to the heart or brain is deemed 'just a flesh wound'-- this goes double if it's the protagonist getting shot, skewered or bitten. The ubiquity of this trope means that many people who have never seen a serious injury in real life assume that a bullet to the shoulder is not particularly life-threatening. This has a problem on two levels. First, people attempting to incapacitate someone in a fight or dole out a non-serious injury for a stunt overestimate how much damage they can inflict before they need an ambulance. Second, people who have sustained an injury are more likely to 'tough it out' thinking the damage is minor when they really need to be getting themselves to a doctor.

At my friend's behest, my analysis is this: get yourself some first aid training. 
Type 'free first aid class + [your town]' into Google, and you will most likely find courses offered by your local hospital or fire department. Many are outside of workday hours, and will allow you to bring kids (you may even be able to get your kids certified as well). Hopefully you'll never have to use those skills, but at the very least you'll have done some good research for your story and you'll be prepared if it ever isn't just a flesh wound.