Yes, internalizing the therapist is definitely a goal of therapy- and the fact that you could carry on that reassuring conversation with yourself as to how you would patch up any potential negative outcome of showing her the mark on your arm, is a good sign. Also, showing her the marks nonchalantly in the first place is another good sign: you really don't need to worry about doing something like that in therapy: it's the perfect space to let go of fear of being too much for someone (too distressing) as well as the typical fear of being judged negatively.

P.S. Did he miss the mark getting your arm? Because.... ouch.