I’m wondering if I successfully filed my state taxes as well as my federal?

You complete your tax return by finishing all 3 Steps in the File section. In Step 3, to e-file your tax return, you must click on the Orange "Transmit my returns now" button. To check your e-file status please take the following steps.

1. Sign in to TurboTax with the same login you used when you filed your return. If 

2. Click Taxes near the top left corner of your screen, under the TurboTax logo.

3. On the My Tax Timeline screen, your e-file status for both your Federal and State will show up. If you see the Orange Take me to my return button then you have not filed your taxes.

You can also check your e-file status using the TurboTax E-File Status Lookup Tool.

E-file tool

You will also receive an email advising you of the return being accepted or rejected. If you opted in for text messages, you will receive that also. 

State tax will not be sent to the state until the Federal tax return is first accepted by the IRS.   That will not happen until the IRS opens and starts accepted on Federal tax returns on Feb 12.   Until then both the Federal and State returns will just sit in limbo on the e-file server.