Is 10 stone 6 (146lbs) a healthy weight for me?

[jombo]

15, male and 5ft 8 which is around 172cms.

[Miserabilia]

http://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Body_mass_index_chart.svg/690px-Body_mass_index_chart.svg.png

Your BMI is somewhat on the high, but it's still around the average.
You're either a bit heavy (But not overweight, still healthy) or muscular.
So on the high side, somewhat on the border of average/overweight.
I wouldn't say you're "unhealthy" though, maybe you just need to loose a little weight. (Or not, if you're muscular)

[Troye]

Yeah, you're fine