I ended up getting it figured out. When you get to the screen that asks you if you filed a tax return in 2018 or 2019, click the box that says "I don't have my AGI from those tax years." It will take you to a screen that will ask for either your IL PIN or your driver's license. You can find your IL PIN by going to this website: https://mytax.illinois.gov/_/#1
On that site, enter your social security number and then in the next field, click "Look up my IL PIN." It'll ask for your driver's license number and then just give you your PIN.
You may be able to avoid all that by just entering your Driver's license number when it asks for either one (on the Turbotax site), but I found it odd that the driver's license would work since I'd just entered it in a few screens before.
Anyhow, using the IL PIN worked because I just refiled and got a text saying IL approved my return.
