After you file

You do not enter a state refund amount on the IRS site.  The IRS is only for federal tax, not state tax.

If you are trying to check on your federal refund then you need the amount of your federal refund from line 20 of your federal Form 1040, your Social Security number and your filing status.

Look at your tax returns and find the amounts on them.  The amounts of your refunds are also shown in your online account.

Did you forget how to access your account?

You have to access your iaccount for yourself using exactly the same account and user ID that you used when you prepared the return.

Many people have multiple TT accounts and forget how to access them.  Log out of the account you are in now.

Account recovery

https://myturbotax.intuit.com/account-recovery/

https://ttlc.intuit.com/questions/1901535-forgot-your-turbotax-online-user-id-or-password

Or did you use the desktop version of TurboTax?  If so, the files are on your own hard drive or any backup device you used like a flash drive.

https://ttlc.intuit.com/questions/1901486-how-many-turbotax-accounts-do-i-have

https://ttlc.intuit.com/questions/1901535

https://ttlc.intuit.com/questions/1901659-find-your-tax-data-file-in-mac

https://ttlc.intuit.com/questions/1900721-find-your-tax-data-file-tax-file-in-windows

To get a copy of your previously filed returns prepared with online TurboTax https://ttlc.intuit.com/questions/1900748-how-do-i-get-a-copy-of-a-return-i-filed-in-turbotax-online

https://ttlc.intuit.com/questions/1900748-how-do-i-get-a-copy-of-a-return-i-filed-this-year-in-turbo...

Here are the sites to check on your refunds.

Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund