I really feel for you, especially since the USA doesnt do bag matching so there is no way that AA can assure you or anyone for that matter that they loaded your bag in the first place.

AA/ QF have lost my bag on 3 out of the last 4 flights back from the USA. In 2 cases the TSA failed to place the bag on the belt after screening and the item was located at the baggage screening point. In the third instance, AA in JFK didnt know where QF 108 left from and so my bag was in lost baggage in the AA terminal. It turned up with the original tag and a BA tag over the top.

On the last occasion the bag was "lost" for 7 days. The second occasion three days and the first 24 hours. In the case 2 and 3 the check in manager at LAX and JFK was sent looking for the bag by QF baggage.

Sadly, AY as the end carrier is responsible and I can share your frustration with what seems like a fruitless task. It is very rare for luggage not to turn up so hang in there.