How do I get my $20 off self-employed version through AAA?

You have to enter TurboTax through the link on the AAA site when you begin your return.  If you already prepared the return it is too late to ask for the discount.

How to get the partner discount

https://ttlc.intuit.com/community/charges-and-fees/help/how-do-i-get-my-turbotax-affiliate-partner-discount/00/26509

So I guess you would need to start over to get the discount.  Try going to AAA and start from there.  Maybe it will let you log into your account so you don't have to start over.