Welcome to FT! Someone will be along shortly to give you the official welcome.
Need some more information. I deduce from your post that you have made a booking with AA for your trip to MEX, and the BER-LCY sector is operated by BA as a codeshare for AA.
If it is an AA booking, then you may get limited help here, although some of the BAEC forum regulars are schooled additionally in some of AA's policies.
The first thing I would do is to try and get hold of the e-ticket receipt, as that will confirm, definitively what your luggage allowance is on the ticket. For a BA ticket, you can get the e-ticket from
https://www.finnair.com/en/customer-...ticket-receipt. I don't know whether this will work if you put in the BA booking reference. There may be a different booking reference for AA.
Have you tried adding a bag on the AA website?