AA platinum is, as I understand it, OneWorld Sapphire - which would grant you access to the BA Galleries business lounges. If you have entered your AA frequent flier number on your booking then your status ought to be on your boarding pass. That, and/or whatever “virtual” cards the AA app provides, should work even if you don’t have the physical cards.
edit: just realised your onward flight is Aer Lingus (I guess T2?), which is not a full OneWorld member and has some funny rules about lounge access even from BA... so you may wish to check with someone more knowledgeable than I!