If I unintentionally bought TurboTax, is there a way I can undo it so that I can start my tax filing over?

No, if you already completed and paid for your tax return, you have to fix it and resubmit it, not clear and start over. 

Here's how to do that:

1. Sign in to TurboTax Online and select Fix my return.
2. On the Let's fix your return and then refile screen, select Fix it now or Revisit.
3. The next screen will show an explanation of what is wrong. If you don't understand the message, ‌ post it here and TurboTax can help you with it.
4. Try to follow the on-screen instructions to fix the problem. 
5. When you're finished, select Continue to File and continue through to refile your return. 
    

What you you buy?  Did you pay for the Online version OR buy the Desktop CD/Download program?  If you got charged back in November that was for the Desktop program Advantage auto renew plan.  

If you return is getting rejected either someone already claimed you as a dependent OR one of your dependents filed a return claiming themselves.  You probably have to mail your return even if the other person amends their return.   And double check all the ssn listed on your return.  

I couldn't see what to do from here even after tapping continue. It would just tell me to review my Federal and State returns but I couldn't change neither of those before resubmitting

If you are still having issues, please call TurboTax Customer service.  Here is a link:  Turbo Tax Customer Service