Yes I would get new tickets now online, and sort it out tomorrow with Customer Relations. Since it's not ticketed it can't no show either. If you had to pay cash then BA is obliged to refund any losses, but if there are Avios available then that's best.

But as ever it's always good to check you are ticketed, either via My Flights in the BA App or with an email e-ticket receipt after the most receent change to the booking.