What Is My Ideal Weight For My Age And Height?

There are a couple factors that go into account, but, as a GENERAL:
Women; for every inch you are over 5' you add 5 lbs (give or take) from 100lbs
example: A women that is 5' should weight 100 lbs
5'1" = 105 lbs
5'2" = 110 lbs
5'3" = 115 lbs
5'4" = 120 lbs
So you at 5'5" should weight some where around 125 lbs (give or take). But because of your young age I would say you could weight as little as 115 lbs and up to 135 lbs and still be considered healthy, but your ideal is 125 lbs.You can calculate t=your ideal weight through this Weight Loss Calculator. Factors to consider are bone density, muscle tone (will make you weight more/ it's a good thing), fat % (women have more fat than guys/that's what boobs all are, and we generally carry our reserve in our hips, guys carry it in there stomach area), physical and mental health etc...
At your age I was only 4'9"(didn't really grow until I was 18, then again at 22.. Late bloomer), I weighted about 100 lbs/pure muscle because I was into so many sports and horses.
I'm now 5'5" but I'm also 25 years old, I weight 127lbs. When I'm more in shape in dip down to about 120lbs, but in general my body stays in the 123-126 range.