Do you have to "define" yourself at all, other than as an imperfect human being, like all of us? We ALL sometimes engage in unhealthy behaviors and have unhealthy thoughts. Every person on the planet has character defects and does things not so good for them or for others.
You are aware of things you want to work on, and are actively working on them. That puts you ahead of a large segment of the population who close their eyes to them.
When you find yourself behaving in an obsessive or manipulative way, use some of the strategies your therapist has given you. People don't change overnight. Practice working on recognizing it and then doing something different. If you find yourself obsessively researching the ex, try researching something else, instead. Don't FEED it, IOW,
Hugs, you may not be progressing as fast as you'd like to, but you ARE progressing.