Yes surgery will cause another scar, but it would most likely be a linear scar and not catch the shadow that your deep scar is most likely catching. Filling this in with Juvederm or Restylane is a good way to go and the results can be long lasting.
Chicken pox scar on nose
It would be possible to surgically remove the chicken pox scar on your nose, but you need to realize that you would be trading scars. The scar that you would get from surgically removing it would ideally be a flat, linear scar. In most cases, this would be less noticeable than a wide, depressed scar.