Since you have already filed your return, you'll need to wait for your tax return to either be rejected or accepted, if it is rejected you can add your Form 1099-G, correct any other errors on the return and resubmit it. If it is accepted, you will need to amend your return to include the Form 1099-G.
Note: You cannot e-file an amended return as this cannot be filed electronically. The form is only filed on paper, so it will need to be printed and filed by mail.
Please see the following TurboTax FAQ for instructions on how to amend your 2016 tax return in TurboTax.