I'm not 100% entirely sure, as I have never had to do this...But I know when you purchase apps (and other items) from iTunes you are able to authorize other computers to use it, I want to say the maximum is 5 computers.
If you open iTunes and click on "Store" on the menu bar on the top (File, Edit, View, etc.) there is an option to "Authorize Computer." You are prompted to enter in your iTunes login credentials and then you click "Authorize."
I assume this will fix the problem for you. However I'm not sure what else this allows your son access to, meaning will he be able to re-download all of the music/movies/applications you have purchased on your own private computer or if he will only have access to the items you have purchased and downloaded on his computer?