Once an E-mail has been delivered it's like a word-document on your computer. If you go out and buy a new computer and monitor, your new documents are not going to make the jump between computers all on their own.
If you still have you access to your account at your old host (gearhost) then it may be possible to move those E-mails over to Dreamhost - but we'd need to know specifics about what webmail set up you had there.
The reason some of the E-mails are at dremahost deals with name servers. When you updated the names server through the domain's registrar records began updating and E-mails were delivered to your DH server instead of your gearhost server. That change can take from minutes to 3 days to happen, and during that peroid some E-mails may have been directed to your old host and others to DH.
art.googlies.net - personal website