One thing I often do if I don’t like my seats and want to change to alternate seats without paying more, is wait until 24 hours before the flight, when many seats are released and don’t cost extra. I’ll even sometimes set an alarm so I don’t forget to get online and do this. This has happened several times when I couldn’t get seats together for my family (my husband and I and our two kids), which was especially an issue when the kids were younger and we didn’t want them sitting alone. It’s not guaranteed to work, but I’ve had a lot of success with this strategy.
If I were doing this…I would choose two aisle seats in the same row. That way you can chat with each other, share food, store medical equipment, etc…but you both have aisle seats.
But really…I would ask if any upgrades are available when you check in. We have been successful getting economy plus or better for no cost…because it’s easier to sell those cheap seats at the last minute than the more exoensive ones.
We most like having two seats, window and aisle in an area designed for just two people. Airlines won’t seat me at an aisle because they don’t want me tripping people with my medical equipment (tho I never had in my hundreds of flights). Anyway, we are fine with what we get and are just happy arriving intact at our destination. 
AA can’t always upgrade at the gate. So maybe ask at the main counter. I ran into this recently.
Yes…check in at the counter…not the gate! And get there early…really early…and ask if there are any better seats available and for how much.