This sounds like you don't even know whether this sector was bought on an AA fare or a BA fare. If it was an AA fare, the fare rules will be the AA fare rules. If it was a BA fare, then they will be the BA fare rules. The fact that you were booked on a BA flight won't itself tell you whether it's an AA fare or a BA fare.

To get the full fare rules, you'd need to know at least the full routing, the fare basis (or bases, if more than one was used to construct the ticket) and the ticketing date.

If you have a BA locator, try taking that to classic.checkmytrip.com and clicking the e-ticket receipt tab if there is one. That might give you the ticket number and the fare basis for each sector of your trip, which could be a start for some guesswork.