Anything is possible with anxiety and how it manifests depends on who we are and our experiences . . .
False memories are indeed possible . . . even people who do not suffer with anxiety can create false memories . . . .for some, it may be a way of trying to get something into your field of perception so you can deal with it; there may be a veneer of reality but it is covered by other layers that are not true . . . for me, I always seek validation in some type of objective reality . . .
Now, if these false memories are overwhelming for you or bother you, a trained professional can guide you in deciding whether your mind is trying to get you to process something or if it is a false memory, how to take it apart and process it . . .
I do not suffer from false memories, but, at times, I think that I remember something . . . it is fleeting snippet from my past but if I cannot validate it, I simply let it go . . . on occasion, I sometimes have the same snippet enter my head . . . . I may sit down and think about it and try to figure out what it might be saying to me directly or indirectly, but usually, I just let it go . . .
If you suffer from OCD, you probably are predisposed to focus on the event . . . . again, perhaps with some professional intervention and guidance on how to manage the OCD with respect to false memories might help . . . . .
Do you keep a journal of these false memories so you can see if there is a pattern perhaps pointing you to some issue that may be triggering them that you need to address?
Sorry I could not have been of more help, but do continue to post and perhaps another one of our community members may have more insight than I do . . . take care, kc