So, @mydomain.com is "hosted" within your computer ?
You need to be MUUUCH more specific than:
"cannot get pop3 to work..."
"its weird because when i login into the SquirrelMail if i send my self and email: firstname.lastname@example.org
then i get the email on my inbox , but i send a email from my hotmail account to email@example.com
i dont get it...."
So, I'll suppose @mydomain.com is hosted within your SquirrelMail. What is happening if that is true ?
When you mail using Squirr., it can easily find firstname.lastname@example.org
BECAUSE IT IS ITS OWN DOMAIN.
When you mail from Hotmail, how does Hotmail servers where to send the email for @mydomain.com ?
I mean have you set your MX DNS records ?