I accidentally filed single instead of hoh with a dependent

No, TT does not automatically change your filing status.   If you made a mistake you will have to wait for the e-file to be rejected and change it, or if it was accepted, wait for it to be fully processed and amend it.

Am I Head of Household?

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-filing-status/qualify-head-household-2021/L0NxUtVc2_US_en_US?uid=m5x19jkx

• What is a "qualifying person" for Head of Household?

If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/taxation/married-person-claim-head-household-filing-status/L078u1RSW_US_en_US?uid=m62dkc4a

In the My Info section of the program when you enter your filing status as either Single or Married Filing Separately and you have entered a qualifying person as a dependent on your tax return, the TurboTax program will ask you a series of questions to determine if you are eligible for Head of Household.

If you entered the information correctly on your dependent and your home situation, then TurboTax would have automatically given you the head of household status.  It would have said at one point  you qualify as Head of Household do you want to accept this status.  If you said yes, then you would be head of household.  If you said no, then you would be single. 

You can look at the front page of your form 1040 to see your filing status.  

If it is correct, do nothing.

If it is incorrect, once your return has been fully processed, you can Amend Your Return to walk back through the personal info section and correct the answers to your questions.