Exporting part of a database?

A while ago I backed up my database for another site and loaded it into a DH database. I am trying to move from my crappy host to Dreamhost - but I don’t want to have to export and shell-up the entire database again. Is there any way through phpMyAdmin to only export the changes made from a certain point in time? Keep in mind, tables have been added and removed. I’d say the old database has about 80% of the new database information, so it shouldn’t be TOO much. Thanks in advance for any help and thoughts.