I filed my taxes in February, paid what I owed the state and received my federal return, now I'm getting emails saying that I have missed the deadline. What do I do?

You may have another TurboTax account that you no longer use so that is why you receive the emails.  Ignore the emails since you have filed both the federal and state return.

Yeah, I get lots of emails from Turbo Tax since I have several fake accounts to test in.