You can see what juries have awarded by going to a law library which may have research materials that show the verdict amounts by the type of case or injury. Additionally, you can research this at verdictsearch.com
Without an attorney, the insurance company will offer you less than with an attorney. I would expect you'll get an offer of $1,500 to $2,000. What an attorney would ask for will depend on other factors besides the medical bills, e.g. the amount of vehicle damage, whether there was medical insurance, what the medical or insurance liens are, etc.
If your son was hurt, you should hire a personal injury lawyer to handle your son's claim against the driver's insurance company. You don't need to file a lawsuit right away and incur all the costs of a lawsuit.
Insurance companies routinely claim that the medical bills are excessive, especially if there isn't much car damage. Your attorney may be able to get the insurance company to pay more or to get the medical providers to accept less.
You should speak with a personal injury lawyer in your area that offers free consultations as most do. If you absolutely want to handle the case yourself, you'll need to get copies of all of your medical records and bills to put together a demand package to the insurance company along with the police report, photos and an evaluation of whether you'll need future medical treatment, and a statement from your employer of any wage loss. It's complicated. That's what personal injury attorneys...