Your upgrade should have been processed and then when you boarded they should have handed you a new boarding pass. But...........
But it this situation - waiting for upgrade on international flight - I would arrive at the gate say 75 minutes before departure.
I check the upgrade list on the AA app (frequently) to see where I am on the list. I use expert flyer seat map to check how many open seats there are and availability to see how many J seats remain (again frequently). If Y is oversold then they may reduced number of J they will sell. The seat map is pretty accurate at 1 hour out.
If I know I will likely clear the upgrade - I will definitely go the gate early. And I continue to check AA upgrade list and EF seat map at the gate, particularly if I have a companion I am trying to get upgraded.