If you purchased a retail copy of TurboTax, you have the ability to create five different Federal tax returns and file them electronically (e-File). If the TurboTax version you purchased included e-filing your state's return also AND you used that function, your son will have to file his state return in paper form (mailing it to your state's tax office). This is the most likely scenario.
Just start the app up again and select New Return to create a new filing. Make sure your son drops his state return in the mail well before the pickup time. Sometimes, the mailperson is early.
Best wishes.
No, you cannot allow others to use your license code. I understand that you would like to help your son, I'm a mom too. That license represents your purchase of Turbo Tax, only you. It represents your ownership of the program. If the license code could be given to others to use then you are basically selling intellectual property illegally.
You can start a new return for your son on your computer, as someone previously suggested. Or you can install a brand new copy of TurboTax in another (your son's) computer using the purchase confirmation you got when you purchased it, and start your son's return there.