Some people are afraid that, if they forget, then the other person’s injustice will emerge again. Others, as in your case, want to forget. When we “forget” in your case, we tend to let the memory fade so that it is not constantly coming up for us and challenging our happiness. I find that as people forgive, they do forget in the sense of no longer having to continually relive the event in their mind. What tends to happen is this: People now remember in new ways and look back less frequently. By “remembering in new ways” I mean that when you look back, you do so with far less pain than in the past. People look back less frequently because, when filled with resentment, there is a tendency to ruminate on what happened in the hope of solving the unpleasant issue. Upon forgiving, you may not have solved the problem, but you have solved the nagging effects of that problem such as anger, fatigue, and sadness. So, it is wise to engage in “forgive and forget” as described here.
For additional information, see Forgive and Forget: What Does it Mean?