Is there a way to display sent/received iMessages in a "horizontal" format rather than the current "vertical" left/right bubble format?
In iOS, aside from using accessibility's large text features, there are no options to adjust the display of messages in the Messages app.
On OS X, all of Message's display options present new messages vertically – each new message appears below the previous one. There are three settings to choose from and only (the default) one displays them in a left/right format.
To change the way Messages displays messages, you have to 'secondary-click' (AKA control+click or right-click) in the blank space between messages. That brings up a contextual menu with only three options:
You can secondary-click in the Messages (main chat) window or in the sample transcript found in Messages > Preferences > Messages.