Since you mailed in your returns, you will not get a message letting you know whether your return was accepted or rejected.  Hopefully, you mailed in your returns with a receipt, so you know if your returns were delivered.

For your Federal refund, you can keep checking the IRS website, Where's My Refund.  It will show information about your return but it can take 3 to 6 weeks to show on the website.  The IRS website updates once a day.

https://www.irs.gov/refunds.

For a State refund, State's differ on how long it takes to issue a refund.  You can check your State's website for refund information.

How do I track my state refund?

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...: