If you only have two developers, you probably shouldn't be using Scrum without very carefully thinking about the intent of each ceremony and artifact and what it brings to your project.
From the Scrum Guide's definition of the Development Team:
Fewer than three Development Team members decrease interaction and results in smaller productivity gains. Smaller Development Teams may encounter skill constraints during the Sprint, causing the Development Team to be unable to deliver a potentially releasable Increment.
If Scrum calls for a Development Team of between 3 and 9 people and you have fewer than 3 or more than 9, you shouldn't be calling what you are doing Scrum.
However, you can take advantage of some principles of Scrum: timeboxes, potentially releasable increments, a daily regroup and replan, planning for a given timebox, demonstrating functionality at the end of the timebox. Extreme Programming also offers some good ideas such as pair programming. You can also look at strategies such as Kanban for organizing and limiting work in progress.
Most defined methodologies are designed around solving problems that come with larger teams. In a group of 2, you may not be encountering those issues. But that doesn't mean you can't follow good practices that make sense for you.
