Is it normal to not get an email if my taxes were accepted?

TurboTax emails you when the e-filed tax return is either accepted or rejected.  This would have been the second email from TurboTax.  The first email would have been when the tax return was first transmitted with you clicked on the large Orange button in Step 3 of the File section labeled "Transmit my returns now".

Check your spam and junk mail folders on your email account for emails from TurboTax.  

Verify that you have the correct email address for your account.

Sign onto your online account - https://myturbotax.intuit.com/

Select Intuit Account from the lower left corner.  This will take you to an Account Settings screen.

To check the status of an e-filed return, open up your desktop product or log into your TurboTax Online Account. You can find your status within the TurboTax product.

If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds

If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund