Unclaimed luggage stays with the airline and gets logged against an on hand reference (similar format to a delayed bag reference eg MIABA12345) however it’s somewhat likely this will end up being logged by AA. Staff at the landside desk won’t be unfamiliar with people needing to claim their luggage, be it items they’ve left or delayed bags that have arrived but haven’t been couriered for whatever reason. You’ll need your bag tag and your passport to prove your identity but they should be able to help you retrieve it.