If you aren't using tmux or screen, you probably should be, especially over SSH sessions. They allow you to have multiple consoles open and switch between them, split window, and disconnect from SSH and then reconnect with all your things still open and running (as long as the server stayed running).
The main screen instance is started with:
screen -S outer_screen
I then create a screen session for that EC2 with
screen -S inner_screen
I pop open new screens with this handy command:
screen -S outer_screen -X screen -t newmachine ssh user@newserver.example.com