This is a purely AA question because BA will relinquish control 24 hours prior to UK departure.

On arrival at MIA, head over to AA and have them pull up your AA PNR (it will not be the same as BA) and make certain that AA shows you as being on an A fare.

AA will reassign you to F (it is not an upgrade as you have an A ticket) if there is A space. If not, you would only then be upgraded based on AA status.

Don't get your hopes up as last second A space is fairly uncommon.