How to add bellsouth account without using outlook or a program like it?

You just need to find out from Bellsouth, what to type in for web access since you're not setting up any program like Outlook or Thunderbird. Its likely to look something like mail.bellsouth:xxxx That puts you on the website and you enter your Email address and password to send or receive your mail.

That's how I access my work email at home, whilst at work we use Outlook.

Here is another option that should also work, http://mail2web.com/ but the server blocking issue might mess it up.

Bellsouth now uses Yahoo servers so you could log into Yahoo and send email out as Bellsouth. Call Bellsouth to make sure its set up properly and you should have now problem using any computer to send or receive email from by accessing Yahoo.