Yes. Look for a same day FLL option and call whoever issues your ticket (AA or BA) to ask for that due to the schedule change. If AA issued your ticket, I suspect you won't have much of a problem if there's a FLL option.

UPDATED: I just noticed we're talking about Christmas Day. AA 'puts the airline to bed' early on certain holidays, so I don't see an evening flight to FLL anymore. That's likely why you got switched to MIA. I'd just take the Uber to FLL and call it a day.