[thopok]

Should I use both the built-in firewall and a software firewall from a different company on my Windows XP computer?

No. Running multiple software firewalls is unnecessary for typical home computers, home networking, and small-business networking scenarios. Using two firewalls on the same connection could cause issues with connectivity to the Internet or other unexpected behavior.
One firewall, whether it is the Windows XP Internet Connection Firewall or a different software firewall, can provide substantial protection for your computer.