Turbotax gets no info on mailed in returns ... so did you mail the return to the correct address ? The fed & state go to separate places so did you file each one correctly ? Are you sure they got the mailed in returns ? Did you use any kind of mail tracking option ?
4 weeks or so after mailing the return you should be able to see something on the fed site :
https://www.irs.gov/refunds
And the state :
What does the state say? Check for a state refund https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
Make sure you are using the refund amount from your actual state tax return and not the combined amount Turbo Tax showed you at the end. That was for federal and state combined.