Can I overcome nature AND nurture with personality?

My parents were both very anxious and my father had some health issues (disc prolapse, kidney stones).
I feel like I'm more anxious than most of the people and also at school during gymnastics lessons I needed to practice longer and harder than my peer to get to the same level.
Can I overcome both of these predispositions with my beaviour (Overcome anxiousness by trying new things, like I started climbing and went abroad; keep exercising and eating healthy). Thanks!