BMI calculator

http://www.bcm.edu/cnrc/bodycomp/bmiz2.html

would this be an accurate calulator that would calculate a teen's calorie intake? according to calorie count my minumum requirement is 1810 while this site says that I need 200 more than that...worst of all it says I need 3340 to maintain if I were very active, and they define that by being active more than an hour a day.

What to trust?

I'm 56 kg (~123 pounds)

5'3.5

and 16 years old...

Yes, it makes sense that your calorie needs would be higher based on your age. CC's calorie count is not accurate for those under 21, so an extra 200 calories sounds completely normal. 

I just entered your numbers on that site and it recommended 2890 calories if you're very active, so maybe you entered something wrong?

Nope I entered them right...though eating 2300 is like my highest...And I do work-out more than an hour so do I really need to consume 2890 calories?

Yes, that's a good average.... if you aimed for anything between 2600 and 3200  that would be reasonable because some days you'll be more hungry than others.  It replaces the energy someone your age/size needs if they do more than an hour of exercise a day and it allows you to grow strongly and healthily.   It shouldn't be too difficult if you choose plenty of enery-dense foods and eat/snack regularly.