If it's truly a minor injury, you may not necessarily get more money going through a lawyer (remember they have to get paid too). I would say do some research online, determine what you think the value of his pain/suffering is, add in any lost wages and his medical bills and come up with a number. See what the insurance company offers, never take the first offer and try some negotiating with them. Insurance companies are ultimately in it to get a signature on a release and they will pay for it if you're reasonable. If they don't come back with a number you feel is reasonable then you can go the attorney route, but I see so many people automatically get an attorney and end up getting less of a payout after attorney fees than they would've gotten by doing some research and negotiation themselves.
Also, you can use the fact that he hit/ran to bump the settlement up a little bit, along with the fact that your son is younger and I'm assuming generally active. If the injury caused him to not be able to do things he would normally do (sports, work, go out with friends, etc) that can also bump the value versus someone who is middle aged and just sits on the couch after work for 6 hours.