You need to learn to tell a story in a

She said, I said format. And let the audience judge. If you don,t have good memory about that ( as I do), you could make certain notes. But for this case, don't waste your time. For future, try not to engage in arguments with people, focus on what are the issues to resolve and what efforts you made to make things better. In the end, what matters more is relationship and people, not really the work itself. When relationship is good they can bear with a lot deficiencies of work and competence. Spend time learn how to loose up and make good jokes, it will work better than hard work in your cubicle.