What you are going through may be worth talking to a mental health counselor about. There are some diagnoses where an unstable sense of self is a component of the disorder. We can't diagnose here and maybe it would help you to talk to someone who can, or someone who can reassure you that you're ok.

Which brings me to the flip side: you are young still. It takes time and experience to become a fully formed person with an identity. And being calm sometimes and then impulsive other times, that's a lot of people. I think our society likes to put people in boxes too much: either you're calm or impulsive. You can be both and that's ok.