First of all, how old are you? Not having a solid sense of who you are is incredibly common, I read it increases over the years and doesn't really stop until you're 50-60.

I relate to a bit of what you said being 27, but also being diagnosed with BPD (which one of the symptoms IS having a severely fractured identity, but several other traits must be present), dissociative PTSD (also involves lacking a sense of connection to a self), and bipolar (can cause shifting moods and lead to not being sure of who is the real you). There are other reasons, of course, but if it's causing a lot of distress, which it sounds like it is, do make a therapy appointment and follow up regardless of how you're feeling the days beforehand and tell her you'd like to discover more about yourself and how to do that.