I\'ve recently gone through the database migration process as outlined here:
https://devcenter.heroku.com/articles/migrating-from-shared-database-to-heroku-postgres<
I was in a situation where I exceeded row count limit.
This answer explained how to list number of rows in each table: http://stackoverflow.com/questions/12701711/heroku-row-count-incorrect
Very valuable to know.
You can get into the psql console through terminal, the connection settings are listed on heroku dashboard for your app!