The shots themselves are good in terms of composition and, if you feel that you're struggling with noise, then there's only one solution: a zoom lens with a constant f/2.8 aperture.
At f/2.8, you'd be letting in four times as much light as your 18-55 does when racked out at the 55mm position since it's only capable of f/5.6 at that end of the range.
This would allow you to either lower the ISO value from 1600 to 800 and probably bump up the shutter speed a little to better stop the action.
Like I said in your pre-shoot post: if you can't directly afford an f/2.8 lens at the moment, you should at least rent one for the next time you shoot this sort of event - check out
Hireacamera.com and in particular the 28-70 and 70-200 lenses they have there.