Going back to the original question, I really don't see your three points as character traits.
Obstacles to becoming a police officer maybe, but far from impossible to beat.
- You could have some exposure therapy or similar.
- This could easily be rationalised away.
- Well, most people wish they were fitter. Just get out there and do it.
You're likely to come up against far greater problems through police work. It seems like a great opportunity for personal growth.