The answer is, yes you will be able to travel on your passport as long as it is remains valid (in this case not expired). There are no "child passports" in the USA, a child gets the passport which is exactly the same as adult passport, with the only exception it is valid for 5 years.
And if a 5 year validity bothers you for some reason, note that you can (but don't have to) replace your passport again once you turned 16 - you do not have to wait until it expires.
PS. If anyone's curios, in some countries a child's passport is indeed different from an adult passport, and must be replaced when the child turns 16. However it is usually achieved by making the child passport expire at their 16th birthday, so it is rather obvious. As stated before, this is not the case in the USA.