Yep. I think the "book direct" mantra needs to be enhanced to "book direct or with a competent TA with 24/7 support" . I was on a tech flight a few weeks ago, HBO, got cancelled and my TA had me rebooked onto one of the few seats left on the next flight and had me reticketed before we even got off the broken aircraft. Everyone else was scrabbling around and I just went back to the lounge and got my new BP.

Back to the OP - as others have said, you need to go back to your TA - they can rebook you on any AA or BA flight that has seats in your booked cabin available. BA can't help you