Probably not. Although antiviral meds can prevent the spread of flu, physicians usually don't prescribe them as a preventative measure for healthy people. Since there's a limited supply of the Rx, physicians want to ensure that those at greatest risk of flu-related complications receive those doses. So if you have an infant under the age of 6 months, a senior citizen above the age of 65, or someone with a compromised immune system (a cancer or HIV patient) in your home, ask about getting an antiviral medication for your entire family.
Otherwise, bring just your son to the doctor as soon as you notice flu symptoms, such as a high fever, chills and body aches. An antiviral can shorten the duration of the flu by up to two days -- but you need to take it within the first 48 hours of the illness.
To keep the rest of your family safe, make sure they get their flu shots. Also remind them to wash their hands often, and wipe down common surfaces -- like door knobs and the remote control -- daily.