I accidentally chose the self-employed upgrade and didn't want to. Can I get out of paying the $120 upgrade fee?

You can try to downgrade to a lower version but you will have to clear and start over.  If you have registered you might not be able to clear.

https://ttlc.intuit.com/community/downgrading/help/can-i-downgrade-to-a-lower-priced-version-of-turbotax-online/00/25591

If you have registered or it won't let you clear to start over you can just abandon this account and start over with a new account.  How to start another return in the Online version

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-start-another-return-in-turbotax-online/00/25596

Or see if you qualify for the Free File program.  You can start it at a special website.  It may even bring over your return so you don't have to start over.  Click on Sign In at the top right

https://freefile.intuit.com/

How to switch to the Free File website

https://ttlc.intuit.com/community/downgrading/help/how-do-i-switch-to-turbotax-free-file-program/00/26264

Or one thing you can do is buy a lower version of the Desktop program like Deluxe.  Then you can switch from Online without starting over.  You can download the .tax2019 file from online for free and open it in the Desktop program (any version).  And the Desktop program has several other features and benefits over the Online version too.

How to switch to Desktop

https://ttlc.intuit.com/questions/1901476-how-do-i-switch-from-turbotax-online-to-the-turbotax-software