OMG YES! It's so comforting to meet others who struggle with the same thing.
I think our identity lies in the choices that we make. Benign choices that we make at the grocery store. I remember watching an episode of a TV show where a life coach was helping overly-attached twins create identities. One of the first exercises she did was take one of them shopping to a custom perfume shop where you choose the scents and they blend it for you. It was eye opening.
Why do I choose brand X over brand Y? That says something about my preferences and values.
This is how I began to get some sense of identity. Yes, it wavers. Yes, I feel unsure. But I come back to some basic qualities that begin to define me - in a way I came comfortable with.
Developing some sense of identity has been a long struggle for me... 10 years. But I can now dress with a consistent sense of style. Work with my dog with a consistent training method. My grocery shopping list looks very similar and I tend to pick the same or similar items.
What I'm very, very, slowly learning is that I am ME, regardless of what my emotions are doing today or what bipolar mood episode I'm in. Going through a grieving process and coming to acceptance has made a huge difference in my sense of stability and identity. It has improved my impulse control by helping me recognize when my thoughts don't "jive" with ME, and I'm starting to be able to talk myself down when I get all riled up.
It started with a trip to the grocery store.

You can do that!