I can see how that would be frustrating but once you go past flight connections there's no chance of being able to check-in your bags with AA for a flight the following day. The problem here is that no-one was available to assist you with the re-check at flight connections. Was the flight late by any chance?

In that situation I'd have probably not bothered going to terminal A and tried to find a left luggage facility instead.

Not sure there's much to be gained by complaining to anyone unless you want some soothing AA miles thrown at you?