Yes, you have to debug because the other person is not working on a local copy of the code. If you set up a source code repository (with Visual Source Safe or some other source control system) you can each work independantly on your own machines and not interfere with each other. The source control system will make sure that you don't each work on the same code at the same time. Once one of you has finish and checked in your work, the other can get the latest version of all the files for a up to date copy of the code. This is how you work in a team environment.
There are various source control providers, some will cost you (Visual Source Safe, Sourcegear Vault), and some are free/open source (CVS). Most likely, the free ones won't integrate with a development environment the way the others can. You'll have to investigate what you can get and use.