Because you booked separate tickets, BA has no obligation to rebook you free of charge. Had they been on the same ticket, you certainly would have been rebooked.

Other airlines within the oneworld alliance do have a policy of rebooking customers whose inbound oneworld operated flight was delayed, causing them to miss their next flight on a separate ticket. BA is not one of those airlines unfortunately.

However, American Airlines is so the advice above to head to the airport ticket desk might have helped as there might have been some give and take there considering you would have been dealing with American Airlines and not BA.