Hi , I would like to help with this problem.
Have you set up the apple "Mail" application for you new email addresses?
If you don't use Mail or the email address is different from your current used mail provider , it will need setting up .
You need to get your SMTP server from your ISP , try giving them a call to find out .
This may already be setup if you have been using Mail .
You also need your POP server from your Mail provider ,
Note for hotmail users on OSX:
Mail can work with hotmail accounts but it needs extra setting up with free pops.
"if you use hotmail". Mail needs this free pops application tool ,
Free pops must be used for hotmail accounts as they work differently from normal pop email addresses.
This enables hotmail to work on Mail once setup and installed . http://www.freepops.org/en/download-osx.shtml
See accounts in the Mail Application Preferences to add an account and the details , email , password XXXXX pop server , etc .
If you need extra help please let me know