As OW Emerald (BA Gold) or AA F, you will have a bag fee waiver for 3 bags, so that ought to be a non-issue.

You may well be ticketed in the First Class cabin, but may want to check the fare basis to see if you are actually on an F fare basis rather than a discounted fare which books into F. That will not matter in any other respect as First Class is First Class, but it is worth reviewing fare rules.